Just a couple of thoughts........
If 5vr is 13' 1" or taller...not allowed thru tunnel
If truck and 5vr combined length is greater than 50'...not allowed thru tunnel
Otherwise you will need to pay tunnel fee ($15) and have Rangers stop traffic so you can drive down center of tunnel
Then there is the twisty/winding road with at least 5 tight switchbacks/hairpins before you get to tunnel
That is if you are coming from south entrance and going out east entrance
Where are you coming from??
If west side of Park............then drive over to Hurricane (UT9) and pickup UT59 down into AZ (389) and then connect with AZ 89A on into Flagstaff