Tape will work, however for small ember holes I have always used a smidge of silicone or seam sealer. Carry a small tube of seal when wet and you can even make repairs in the rain.
I have never had a problem with silicone. Just a small dab, wet fingers and tool from both sides.
If the homes are a bit bigger then I've often applied just a bit from inside and tooled with the tip wait until semi dry (enough to hold shape under pressure passed skin phase) then repeat from outside ensuring water can run freely over or around repair without inducing a leak above repair.
I've used this technique for holes as large as pinkie toenail. Although my pinky toe nail is small. Alternatively silicone and an offcut of canvas can make a quick long lasting repair.
One other thing these techniques can make repairs virtually invisible are just as easy and almost as fast as tape besides being longer lasting and more durable IMHO.
This is coming from someone who has spent significant time in a tipi as well as living over a year in a wall tent in Canada heating with wood stove. (Side note: a proper tipi is significantly better engineered then a good wall tent.)
Funny thing is most ember holes I experienced were still from the fires outside the tent not the ones inside.
Hope this helps.
Just ripped two holes in my brand new but cheap as waterproof pants over the weekend. My mate, a canvasser (he works with canvas not politicians) suggested "stickyback" on both sides and then heating it to make the glue truly stick.
Not 100% sure what stickyback is but it sounds like the stuff you cover books with. I would assume this would also work with your tarp.
I will investigate further and share my findings.