Appreciate you made time for testing!
I have not flown for real since some years back (due to medical) ,
But i would say thet the procedure I am used to, of corse depending on the AC & Equipment, I do the following:
I am in either GPS, NAV or HDG Mode (or flying without all that..by hand haha) Set or activate the LOC/ILS frequency to be used and check that the LOC and or GS comes alive.
I Then do an intercept to the LOC Centerline ("feathers") at an angle below 45 Deg, and then ARM approach mode by pressing the APPR button. If HDG was used, Both HDG and APPR arm annunciators should light up, and the autopilot should stay in HDG mode if you are some way out from the LOC. It should then intercept as the localizer comes alive (Needle starts moving), Generally the autopilot should start the turn at about 2 to 3 dots on the CDI. This might differ dep on equip.
Yes, in my experience the distance to centerline does matter. If you are very close, or even inside the feathers (LOC AREA), normally it will capture directly and turn.
I Also tested the ANALOG BONANZA now in MSFS2024 as well, and the problem is the same. Including the need to Switch the AP Nav source to RNAV and Back, AFTER the needles start to move. Then it would capture.
Regarding multiple tries with the KX155's Only, It works every time for me so far... maybe teste 3-4 consecutive approaches .
Insane that it just suddenly worked with the standard procedure!
Anyways, Thanks alot! I will continue testing as well.