Anyone know anything about gas fireplaces with electric switch starter?

[Warpy]

6. It's holding the thumb switch down long enough for the sensor to heat up

that dissuades me from relighting a lot of pilot lights, so I'm with you there. I have arthritis and things get painful fast.

However, what you have is most likely either a wiring fault or dirty sensors. Percussive maintenance might work for a little while, but it won't work for long and given the nature of glass, should definitely be discouraged.

You're going to need a professional to come out and check the system. It's likely an easy fix once it's diagnosed.