Why would a motorcycle without electric start need a battery?

I recently bought a 1980 Honda xl250s dual sport that has been parked in a shed for 5-6 years. I have been tinkering with it and riding it and running it and it all works fine except the turn signals don't work and the brake light doesn't work. I haven't had a battery in it because the one that was in it was dead and I haven't bought a new one yet. I'm curious if that's why the turn signals and brake light won't work or if I'm going to have a wiring issue? And if the battery doesn't do anything for the turn signals or brake light why would it need a battery in the first place?

Yes, a missing battery would be the reason the lights don't work.

Because it has lights and the tiny alternator needs a backup. Probably produces almost no voltage at idle, hence the need for a battery "buffer" to power the signals and brake light when they need it.

Have you checked that the signals and brake lights are actually wired in and not disconnected?

No battery… Nowhere for the alternator to run the charge. Put a battery in the damn thing if you don't just junk it.

For the Ignition… And the tail/brake lights etc. Until 2010, I had No motorcycles with electric start. If I removed the battery from, say, my '78 Triumph, it would not start. Some old Brit bikes used a very large capacitor for ignition. First kick charged it, the second discharged it into the coil.

An alternator or generator needs a battery for a reference and a current "sink" as we call it. A car alternator running without a battery can put out 18 volts and damage anything electronic.

A motorcycles boost-regulated hot-rod magneto-type "alternator" may not put out anything at all, otherwise. Even a very low battery will work.

Only some mopeds that are total magneto don't require any battery. The output varies like crazy though from almost nothing at idle to too much at high RPM

The ignition still needs current. And if you understood how it works, the tickler coil in the alternator needs external current from a battery to produce any current. Or, it's a broken feedback loop. Like, green plants producing oxygen but requiring carbon dioxide, water, fertilizer, and sunshine to do it. Remove one element like sunshine and loop broken, little to no oxygen.

If it has an alternator, which is lighter and puts out much more juice than a magneto, it needs a battery. Butcha can re-engineer the bike with a magneto if ya want. All it takes is time and money.

The turn signals, brake lights, etc run off the battery. Put a new battery in it and they will probably work.

Need battery to complete the circuit from alternator. Also, need battery for initial spark to get it running.

To run your head lights fool!