The phraseology "WANTS BEARING..." is in the third person in place of what was surely  heard over-the-air in the form of a request, "PLEASE TAKE BEARING ON US..." (as repeated a half-hour later at 0645 IST), thus AE was invoking Half-Duplex RDF, intending to obtain guidance from Itasca ('DF steer'). 

The "ON 3105 KCS" part of the message may seem to be redundant (tantamont to saying, "listen to me on the frequency on which you are now listening to me"), but it calls attention to a critical issue. 

Critical Issue {1}:  As mentioned in the puzzle,  three different radio frequencies would be called out by AE (3105, 6210, and 7500 KCPS). 

Solvers should take note that in the 0615 IST transmission, we see the phrase "ON HOUR," which was a mere confirmation of the schedule -- but only as perceived by AE.

Critical Issue {2}: Fifteen minutes after 1745 GCT, the time on board the Electra would read 1800 GCT, which is indeed "ON HOUR"; however, that time would be read on board Itasca as "0630 IST," thus on the "half-hour." 

The clause "WILL WHISTLE IN MIC" receives considerable attention in references about the flight.  Conventional procedure for Half-Duplex RDF is for the pilot to key his or her microphone and count forwards then backwards while the operator on the ground turns his or her loop antenna to obtain a 'null' for the bearing.  Several authors express the opinion that AE used her voice at high pitch to simulate an audio tone heard in Morse Code. 

The phrase "// APPX // WHISTLING" probably is another case of using the third person to describe events in the transcript.  However, we are reminded again of something potentially more significant.

Critical Issue {3}: According to some references, AE did not understand Morse Code.  Others aver that both AE and FN were competent with radiotelegraph, but preferred radiotelephone instead.

The phrase "PLEASE TAKE BEARING ON US" was consistent with the 0615 IST transmission, as AE continues to invoke Half-Duplex RDF, obtaining guidance from the ground ('DF steer').   At this point sophisticated solvers are able to identify another critical issue.

Critical Issue {4}: No acknowledgment is present in the transcript that AE had received a bearing from Itasca in response to her 1745 GCT request a half- hour earlier. 

Apparently unknown to AE, the radio operators on board Itasca did not have the appropriate RDF equipment to take bearings from AE's signals on the frequency she was using,  3105 KCS.   Of course, the operator in the radio room would have made no secret of that inability during Itasca's transmitting time-slot at 0630 IST, and therefore AE should have received that unhappy news at 1815 GCT or more likely earlier.  Accordingly, the absence of an acknowledgement in critical issue {4} provides indirect evidence of something more general to concern us.

Critical Issue {5}: Transmissions from Itasca on 3105 KCS cannot be received by the Electra.  Not knowing that, AE goes ahead and tries again.

Critical Issue {6}: On board Itasca, "IN HALF HOUR" means transmitting the RDF response at 0715 IST, which is at the beginning of the Electra's next transmission slot and a violation of the pre-arranged radio schedule.  If AE really said. "ON HALF HOUR," the RDF response from Itasca would not be transmitted until 0730 IST, which is delayed a full 45 minutes.

For unknowable reasons, AE changed from "WILL WHISTLE IN MIC" to "I WILL MAKE NOISE IN MICROPHONE," possible on the assumption that her attempt a half-hour earlier had failed.  If so, AE may have also decided to allow more time for the RDF to be processed. 

The estimate "ABOUT 100 MILES OUT" at 1815 GCT would be doubtful, given previous estimate of "ABOUT TWO HUNDRED MILES OUT" only thirty minutes earlier at 1745 GCT.  Solvers of the Wages of Flight puzzle will probably not classify this is a critical issue for Simplexity Aloft. 

Critical Issue {7}: The simple fact that the message was logged in the Itasca radio room at 0742 IST means that operators in the radio room were listening not transmitting on 3105 KCS during the time slot assigned to Itasca. 

A speculative answer may be present in the sentence "WE ARE FLYING AT ALTITUDE 1000 FEET," which suggests that AE may have been distracted from radio direction finding while engaged in the descent from cruise altitude (possibly through a cloud deck).

Here again, we see evidence of the most serious difficulty faced by AE in the phrase, "UNABLE REACH YOU BY RADIO"  (see critical issue {5} above).

The fuel consumption rate was higher than planned as the result of realities that will be well understood by solvers of Live Reckoning.  Nevertheless, less than 20 hours earlier, the electra had taken off with 22 hours of fuel on board.  AE's worrisome statement "GAS IS RUNNING LOW" probably does not qualify as a critical issue for our solution to Simplexity Aloft.  It is not too unlikely that AE was trying by those words to intensify the pressure on the radio operators on board Itasca.  Either that or she was just thinking out loud.

Almost certainly the statement "WE ARE CIRCLING BUT CANNOT HEAR YOU" was taken down in error.  "Circling" does not make sense according do Gillespie.  Instead the passage should have been corrected to read "WE ARE LISTENING BUT CANNOT HEAR YOU."   If so, that is a devastating reminder of critical issue {5} above.

The next request "GO AHEAD ON 7500" indicates a peremptory change in frequency by Amelia Earhart and another source of confusion.

Critical Issue {8}: The "go ahead" could refer to the frequency for listening by Itasca to hear audio "noise" (formerly "whistling"), but "go ahead" could more likely refer the frequency for Itasca to use in responding with the RDF bearing.

One resource, TIGHAR, offers an intriguing explanation for the loss of radio reception on board the Electra and thus RDF .  As indicated in the cutaway diagram below, supposedly a "belly antenna" was needed for receiving radio communications.  Film evidence has been discovered suggesting that the antenna was torn off during the take-off roll at Lae.  Other experts, especially Rafford, say instead that the V-antenna on the mast atop the aircraft was used for both sending and receiving.  Let us take AE's 1930 GCT transmission, which included the passage, "WE RECEIVED YOUR SIGNALS," as confirmation.

The full sentence "WE RECEIVED YOUR SIGNALS BUT UNABLE TO GET A MINIMUM" implies that AE had suddenly switched from Half-Duplex RDF and was attempting to accomplish Receive-Only RDF, which calls for receiving the 7500 KCS signal using the Electra's loop antenna "to get a minimum" for a bearing. 

Solvers will note that only two minutes had elapsed (0758 - 0800 IST) since AE's request to GO AHEAD ON 7500 -- only two minutes to GET A MINIMUM on a different frequency (7500 KCS,changing from 3105 KCS). 

Critical Issue {9}: Amelia Earhart failed to achieve Receive-Only RDF.

AE returns to Half-Duplex RDF with the statement "PLEASE TAKE BEARING ON US AND ANSWER 3105 WITH VOICE."  The dire truth: Half-Duplex RDF had not worked for more than two hours; there was no reason to expect it would work now.  Or ever.

1. WE ARE ON THE LINE OF POSITION 157-337 ~~ An incomplete position report, given that the sun LOP stretches both north and south of Howland, then...
2. WILL REPEAT THIS MESSAGE ~~ An awkward redundancy, as it might have pertained to 3105 KCS, were it not interrupted by...
3. WE WILL REPEAT THIS MESSAGE ON 6210 KCS ~~ An abrupt change in the Electra's frequency, which is condradicted by its being transmitted on 3105 KCS;
4. WAIT LISTENING ON 6210 KCS ~~ An unnecessary request inasmuch as Itasca would be transmitting on all frequencies during its assigned time-slot, and finally...
5. WE ARE RUNNING NORTH AND SOUTH.~~ An ambiguous -- indeed -- an impossible flight maneuver and altogether useless for guiding subsequent searches.

Critical Issue {10}: Amelia Earhart was woefully uninformed about the operation of her radios both for navigating and communicating.  Or something else...

...which taken together provide more than enough causes for the utter failure in radio communications during the last two and a half hours of the flight. 

The expression "more than enough" should raise suspicions. Arguably the researcher with the best credentials, Paul Rafford, Jr., has used evidence obtained over seven decades from contemporaneous sources for his own speculations in Amelia Earhart’s Radio: Why She Disappeared.   Rafford suggests...

• That the confusion in Earhart's radio work was intentional.
• That both simplex and half-duplex RDF were deliberately defeated.
• That Earhart and Noonan had a destination other than Howland.
• That the Electra would be concealed from all the inevitable searches.
• That Earhart and Noonan would therefore not be immediately found.