Welcome to the forums, newcomer!
It could be possible that the laptop might be suffering from a short(in the circuit) internally where you add pressure, as you've pointed out. It could even be that one or more connections on the laptop might be compromised/weak/loose or that the battery itself is faulty or failing. In retrospect, the battery for the convertible laptop, is located directly under where the trackpad is, meaning that it could very well be a loose ribbon cable or a short of sorts.
You could disassemble the laptop and check to see that all connectors are secure. If you're outside warranty period and you can't disassemble the laptop, best take it into a certified repair center for your laptop and explain the issue to them.