Read up on your lights and understand the total peak draw for each in amps - then make sure the 1 wire in your 2:1 split is sized appropriately to support all the stuff drawing on it. For example, my googling shows the s2 sport as a .9 amp light and you have 2 of them, so draw for the pair would be 1.8 amps (2 for convenience. You will be looking for stuff rated to handle 2 amps or more.
You could basically get away with anything in terms of wire size - I would probably personally run a 12g marine wire because that is what I have laying around. It would more than handle these two lights!
As for the connectors and that debate - everyone has an opinion. I personally like the convenience of quick disconnects so I like connectors. That said - I have had wires pull out of them and it can be a pain to fix. Some say soldering wires makes them more brittle - but I have never experienced this. If a permanent connection is what I am after, I saw an instagram ad for these and have since been fully converted: heat shrink / sealed / soldered butt connectors
As for connectors - you could always look for smaller connectors to get the job done. When I was building my motorcycle harness, connectors were a big challenge as they are massive and you have small amounts of space to hide wires in. I ended up buying the mini connectors from Revival and a handful of these. The whole motorcycle is lit in LEDs so I suspect it is similar amperage. The larger ones say they can handle 40amps, the small ones can handle 4amps but can’t take 12awg wire. These are tiny though - not much larger than a regular crimp fitting male/female disconnect you would buy at the auto parts store and that only connects 1 wire. Here is a tiny little harness component I did - this is the 3 or 4 pole mini Mizu style with some 20awg, a crimp connector, and heatshrink.
If you’ve read this far, you deserve the following: