What's happening with the G3X?

Hmm…
I certainly can’t argue with your point from a technical standpoint. However it does seem like with other Garmin systems in MSFS, the indicator does swing towards the direction of the localizer signal. Perhaps they are incorrect?

The specific airport where I have been testing this is Baltimore-Washington (KBWI) - runway 10, localizer signal 109.7.

To be clear, the plane does intercept the signal correctly, aligns itself horizontally and follows the glideslope down precisely irrespective of the G3X indicators, or lack thereof.

Update:
Just double-checked my observations. On the X-Cub there are both lateral and glide-slope position indications for the ILS. The heading indicator represents deviation from correct lateral position both with the little horizontal green diamond indicator and with the split needle method - not very intuitive, especially if it is pointing 90 degrees or more in the wrong direction. The glide-slope indicator is represented and works as expected.

On the VL-3, basically the same as above for the X-Cub except the glide-slope indicator seems to pop on and off the screen intermittently, probably relative to the proximity of the aircraft to the actual glide-slope.

On a G1000 system, I.E. Cessna 208, the heading indicator does in fact swing towards the source of the localizer and glide-slope signal, using the split needle as an indication for deviation from the target lateral position. It has the same indication as the G3X for glide-slope.