You have to use a crepe paper type tape that is made to bend curves. 3M 233+ tapes are the best, we have them in 3/4", 1/4" and 1/8" wide for taping off rails and pinlining. We also sourced a great alternative blue tape that's not as expensive as 3M products.
So you can use the crepe paper tape to define your outline then use cheap masking tape and newspaper to cover the areas you do not want painted.
Also, blow off the blank or brush it off real well before taping so it sticks well.
Yes... the tape's too wide, and does not want to bend. As stated, the simple solution is thin tape. But if you can't get it, you can also get wider tape (like 1") to lay flat by making relief cuts where the tape needs to bend the most.
Holding the roll of tape low and out behind your head with one hand, and the other hand out in front of you placing the tape and smoothing it down, pull and stretch the tape. You'll be kind of standing like an archer pulling back a bow. Focus on laying the tape's inner edge exactly where you want it, and don't worry about the outside edge... it will tend to curl up. Once the inside edge of the tape is down and tight, go back with a razor blade and cut the outside, curled up edge, making relief cuts so it lays down and adheres to the board. Then go back with smaller lengths and tape over the relief cuts. Just make sure that inside edge is smoothed down tight.