As it stands right now when you get the test drive for a vehicle battle pass once you accept the battle pass level the timer starts. The only way around this is to not advance in the battle pass until you want to use it.
What i would like to see is that its more like a coupon that expires at the end of the battle pass or if you reach the vehicle level. This way you can still progress through the battle pass and come back to the test drive a bit later and not just have it expire.