If your highbeam indicator is coming on faintly when you only have your lowbeams on you may have a problem with the stalk switch (the switch assembly on the column).

A bad fuse or relay is not likely going to act as a timer and allow the only one light to turn on after a couple minutes - they do not work that way. The wiring from the donor car may be suspect. You need to review all connections and pull apart the split loom and look for problems.

If possible, obtain an extra steering column switch to swap in for good measure.