Nope. Dont hack it like that
Make an external gear box and place in it all the extras (ideally everything that does not pass ignitor voltages through it, so exactly the switches and hot restrike module). Wire between the box and lantern with a multicore cable with as many cores as required for your circuit
I'm thinking of doing something similar, but I want the connection between the lantern and the gear box on a plug and socket. For a simple 3-core cable (live, neutral and earth) that's not passing ignitor voltages, I'd probably use an IEC connector. But for something that needs 4 or more cores, what is a good (and safe) connector to use..?