Sure thing, full compressed save folder with all files here: https://www.dropbox.com/s/2mtu4b08spnlmcp/default.rar?dl=0
Craft file here: https://www.dropbox.com/s/459d3ytyafbucfb/Test.craft?dl=0
Exact steps below:
1. Start with clean install of KSP 1.12.3 (completely deleted old folder, reinstall all of it from steam).
2. Install module manager (4.2.2) and throttle limit extended (the beta you provided) via manual download.
3. Start up KSP. No noticeable issues, module manager reports 30 patches during startup.
4. Start a new save in sandbox mode. All settings, name of save file etc left at default, with the one exception of setting probes to requiring control (given that's what this orients around). Difficulty setting for throttle limits are left at default, with only throttle limits activated, global thrust limit window is not touched at all.
5. Go direct to VAB, create a vessel called "Test" (the one in the craft file), starting with a probe core with an aerodynamic cone, second stage with one fuel tank and terrier engine alongside, kickback booster with four controllable fins and T12 decoupler. Save the vessel, click launch.
6. Activate first stage, let booster run full. Wait until vessel has left atmosphere.
7. Activate second and final stages. Time warp to near apoapsis. Burn terrier engine until escape velocity from Kerbin is reached. (Two details that may be worth noting here - I used physics warp to speed up the burn, and used map mode (as in pressing m, not switching to tracking station) to check when I had reached an escape trajectory. I'm fairly confident the physics warp did not affect things, as a). there was no noticeable distortion of the vessel, and b). when I first noticed the issue in my normal playthrough, I had not used physics warp while flying the affected vessels. I'll do another test with no use of physics warp to make sure.)
8. Time warp until the craft has left Kerbin's SOI and is in orbit around the sun. (At this point, the vessel has no electrical charge or signal, and is firmly marked as "no control" in the top left.)
9. Press left-shift. The engine is activated and cannot be shut down using l-ctrl, x or right-clicking the engine and shutting down. The engine keeps burning until fuel is exhausted and then flames out as usual.
I'll see if I can put together a narrated video also (haven't done so before so need to get the software etc set up).
EDIT: Just ran another test, few extra bits to note:
- Activating the engine through l-shift when out of signal sets the engine to maximum thrust rather than low/minimum. (Activating via z also sets it to maximum.)
- Tests were all run with SAS activated at the launchpad and kept activated throughout. (I have now run the test with no use of SAS - same issue, no differences.)
- Burns were activated and ended via the z and x buttons respectively.
- The issue persists even using no physics warp and not switching to mapmode in flight.
