I'm not with Laminar Research, just a fellow simmer in the UK, but I was having exactly the same problem as you in the Cessna Skyhawk, Beechcraft Baron 58 and the King Air C90B.
Basically whenever I depressed the joystick trigger to apply the brakes and then released it again, it would also somehow toggle the beacon and strobe light switches off.
If I held the brakes on, then the beacon and strobe lights would work normally, but as soon as I released the brakes, both lights would be switched off!
Activating the parking brake from within the cab or pressing the 'B' key on the keyboard, did not cause this problem??
I couldn't find much at all about this problem in any forums, so started by taking all of my plugins out of the C:\X-Plane 11\Resources\plugins folder and lo and behold, both the beacon and strobe lights worked perfectly no matter whether the brakes were on or off!
Eventually by trial and error, I found the culprit to be the XPUIPC plugin and when I put all of my plugins back into the C:\X-Plane 11\Resources\plugins folder (except the XPUIPC folder) everything worked as it should.
I then found the following website where I could download a later version of the XPUIPC plugin (ver: 18.104.22.168), installed it in the Plugins folder and the problem was fixed:- https://forum.fsairlines.net/viewtopic.php?t=9287
Something not quite right with the original XPUIPC folder (ver: 22.214.171.124)??
Hope this helps :-)