After installing my led headlights, I went down to get a warrant of fitness for my bike and of course it failed cos the taillight wasn't going was it!...bugger! So I came home and checked the fuses...ahhh, a blown fuse!...put a new one in and turned the key and 'POP'!...it blew again....must be a short then....took the headlight out and put the parklight bulbs back in and hey presto...fixed it...those contacts which the parklight pushes between are very close when there is no bulb in there!
I'm going to try and seal one of the leads into the bulb connector and see if that works. otherwise a piece of plastic shim .025" in between them should do the trick. I can see why they do touch with the bulb out.
When you put the led headlights in, you mentioned there was no parklight so you taped up the wire...there is the problem. Because the parklight bulb is a push in type, you need to leave the bulb in and then tape it because the contacts inside(Where the bulb pushes in) will touch and short out.....I know, cos I did it too!..it dosnt hurt if you leave the bulb taped up and tucked in the back behind your leds...hope this fixes it.
When I replaced mine I took some liquid electrical tape and gobbed it into the park light bulb holder, making sure it went down between the contacts. when it dries it will insulate and seal the connections from getting any corrosion or shorting out. If I ever put regular bulbs back in (don't know why I would, but...) the liquid electric stuff pulls out nicely leaving bright shiny contacts! Works much better than tape and no worries about the shim vibrating out or the contacts building corrosion.
I never had a problem when I put in my LED headlights. I simply left the park light in its socket and tuck it out of the way in the housing. The park light fits pretty tight in the socket, so I didn't feel the need to tape it up. If I think it will be a problem, I have some larger heat shrink material that will nicely fit over the bulb and socket allowing me to heat shrink the whole thing.
I may cut the socket out and tap into those wires for some colored led lights I'll locate under the tank. Not sure if that little park light was on all the while the old headlights were on or just when the key was in the park position. I'll have to check that out.