A problem regarding my Slayer Exciter circuit?
But why do I have to touch my light to the wire initially?


You need to create a situation where the electric field across the tube is big enough to start ionization. Your circuit is battery powered and appears to have very little ground capacitance hence your body makes a very feeble connection to the "current return path" of your circuit. Given that your body is actually part of the circuit, this feeble connection is the weak link in my opinion.

I would connect the negative terminal of your battery to a piece of tin-foil (aluminum foil) that forms a 12" ground-square under your base board. Now you have a significantly increased ground capacitance and a less-feeble AC connection to your body. This will improve things.

However, there is no guarantee that your circuit is producing enough voltage so although the ground-square may improve the situation, you may still need to adjust the output coil.