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Can you lift the end of the current tape up a bit? Is it thick and/or multi-layered?
If so, then it might be worth a punt on new tape for (I paid £4 for two rims of Velox). I've got a whole roll of that yellow tape - same as Stan's - for when I was trying to get that stupid front wheel to work by converting it to tubeless. You're welcome to a rim's worth if you can be arsed getting it from me. I'd imagine your nearest bike shop would have a roll of Velox you could experiment with. You might be able to use a skinnier version, so long as it covers the rim holes.
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The Yellow shit I have is Tesa Tape 4289. It worked for my tubeless install but I never got to ride that wheel as the frame died beforehand.
Actually, that's wrong, I bought Tesa tape but I used DT Swiss tubeless tape:
https://www.ebay.co.uk/itm/DT-Swiss-Tubeless-Rim-Tape-All-Sizes/231988917903?epid=1765833996&hash=item36039df68f:m:mOpqqAhAPywUYROeVTXRHZQ:rk:1:pf:0Way more expensive but I think I'd already ordered it before I found out about the cheaper Tesa tape.
I use Velox most often because it's basically what I've always used. I'm basically a dinosaur now though, in terms of tyre setup. The yoof can have their jizzy tyres and their plastic rim tape, I'll stick with what works for me until the alternatives are better.