I would suggest in this case you to select a thick rubber rim tape.
There are several types of rim tapes: for single-wall rims and for double-wall rims.
Double-wall rims have large holes through which the nipples have been inserted. Because of this, the double-wall rim tape has to withstand great pressures. It's the only support for the high-pressure tube at those large holes. Thus, for double-wall rims you use fabric tapes. Historically some have used Velox rim tape that's made of cotton I believe, but there are more modern rim tapes made from synthetic fabric. I use Ritchey rim tape. When buying the rim tape, the important properties are rim diameter, width (ideally the tape is so wide that even if pushed to one side, it won't show any part of the hole at all) and pressure it can withstand. Obviously for adhesive rim tapes you cut yourself, the rim diameter is not a major consideration: the tape just has to be longer than the rim, but how much longer doesn't matter.
Single-wall rim tapes have different properties you need. In single-wall rims, the purpose of the rim tape is to protect the weak inner tube from the nipples and maybe the protruding spoke ends. In this case, you don't need high-pressure support. In fact, the rim surface, the nipples and the sharp spokes protruding through the nipples can perfectly well support any pressure the tube can hold. However, the shape of the nipples and spokes protruding from the nipples is such that the inner tube may not like being bent to such a strange shape around a sharp object, and the inner tube thus may become damaged. In this case, you want the rim tape to be soft and conform to the sharp object on its lower side, but still be smooth at its upper side. This means the material should be rubber (the same material that inner tubes are made of), and the rim tape should be quite thick. The rubber rim tape in fact is damaged by touching the nipples and spokes, but this doesn't matter as it doesn't hold any pressure. So the rubber rim tape is a sacrificial material: you want the damage to be limited to this rim tape only, and not be extended to the tube.
Also, today tubeless is becoming very trendy. I'm not going to use tubeless tires ever, but the tubeless fanatics that are prevalent on this site can probably tell much about what kind of rim tape tubeless tires need.