Running a lead directly to 10A lead on fusebox

It's an '83 XJ750 with the full factory fairing.The wiring on this thing has been a rats nest since I bought it. The wiring for the headlight ran through a multi-pin connector on the fairing, to make it easier to take off, and to accommodate a radio, CB unit or whatever.
The running lights haven't worked since I bought it. Since I needed to fuss with the Atari and replace a turn signal unit, figured I'd fix that as well.
My biggest mistake so far was assuming that the solid black wire on the new turn signal was the ground. Entirely my fault. Len sends a printed sheet detailing which leads have which functions. Big waste of time.
I'm replacing connectors and using shrink-wrap tubing along with dielectric grease, so it'll be weather-prooof.
I can't find any hot wires with bullet connector ends (other than the flasher leads).
Is there any reason why I can't run a wire to the fuse box (updated with blade-style fuses), put a "T" fitting on it, and run a short section to each running-light lead (the black wire) and then ground through a ground (black) wire?
Will the 1034 bulbs pull too much current? I can't imagine that they would, and don't want to spend the $ 30 to 45.00 to switch to appropriate LED's, if I don't have to. Did just throw a new flasher relay on, so LED's are a possibility.

 

P=I X e so 10A times 12 volts is 120 watts
your highbeam is about 60 watts
10A is more than enough, 5 should do.