Yeah, you really want to cover the whole width or even slightly wider so the tape goes even slightly up the side of the rim just a couple of mm, ideally (32mm tape on 30mm rims is great).
The secret is the tire beads need to sit ON TOP of the tape.
If you do that, the whole inflate a tube overnight to press the tape down dance is totally unnecessary.
If the tape is sandwiched between the tire beads and the rim along the outside edge, it will seal and pressure of the air in the tire pressing the rim beads onto the rim provides plenty of pressure on the tape.
This was the key for me. If the tape is narrower than the rim and you're just relying on the tape being stuck to the area around the spoke holes, you're gonna struggle.