Yes, you can re-warp with regular electrical tape, or get some braid - painless sells a kit for that too.
Rewrapped harness with non sticky black electrical harness tape. If you dont have time to do it right, when are you going to find time to do it again.
I recommend that you DO NOT USE regular electric tape. You don’t need to buy it from Painless, but use a non-sticky tape that fuses with itself. Electric tape does not hold in a warm environment over time.
In ‘96 I used ‘Magic Wrap’ from Home Depot... it’s still standing up well. I’ve also used 3M tape designed for the purpose. Electric tape will become a sticky mess in no time.