The '78 models had a few changes in the wiring compared to the earlier models. '78 was the last year for the headlight on-off switch on the right handlebar control, and the first year for the auto-on headlight relay. This meant that the handlebar switch only worked with the key on, motor not running. As soon as you started the bike, the auto-on relay would kick in and bypass the handlebar switch, turning the headlight on no matter what position the switch was in. I thought that was a rather silly set-up so I looked into "fixing" the handlebar switch, returning it to a fully functional (at all times) state. It turned out to be rather simple, just by unplugging one wire down at the relay ......
The relay is still "doing it's thing", trying to send power to the headlight, but that signal no longer goes through now.
'78 was also the first year the tail light was wired directly to the ignition switch and is controlled by it. Earlier models had it connected to the headlight on-off switch so you had control over it. Now it's not too big a deal on the models with a single tail light bulb, but some of the later Special models added a 2nd tail light bulb and also two license plate illumination bulbs. So now you're turning four bulbs on with the key. My '83 came like this and I didn't like it. I think it's too much draw on the rather small battery these bikes came with, so I "fixed" it. I added an earlier right side handlebar control with the headlight on-off switch, and modded the switch plate in the ignition switch so the tail lights didn't come on with the key any more. Details are here .....
https://www.xs650.com/threads/retrofitting-headlight-on-off-switch-to-81-83-model.58167/
And eventually, I "fixed" my '78 as well by changing to an older ignition switch, one that doesn't turn the tail light on. Before doing that though, I changed to a L.E.D. tail light bulb to reduce the draw when turning the key on. But this caused another minor issue. Apparently the draw is so small with that new bulb that the light checker thought it was burned out, lol, so it turned on the dash warning light. I fixed that eventually by just removing the light checker, but until I did that, I just pulled the bulb out of the dash light, lol. The light checker is difficult to access, being mounted on the back of the battery box. You need to remove the rear wheel and the plastic inner fender.
So, let's talk about the light checker a little. There were two versions used, the simple 3 wire unit like my Standard had, and a more complex 7 wire unit used on the Specials. The simple 3 wire unit only monitors the brake light and removal is easy, you just unplug it and toss it, no jumper wire required. However, the more complex 7 wire unit monitors both the tail and brake light, and power for and to the tail light runs through it. To do away with it, you need to add a jumper wire to restore power to the tail light.