As mentioned, the Going to the Sun road is a lot tighter. If your truck is a dually, it will be very tight in some spots with absolutely nothing on the passenger side while going up.
I went up/down twice in a long box single rear wheel truck no problems at all, though it wasn't tourist season so not a lot of traffic. If it was very crowded, would still be doable.
Problem is, there are very few places to stop and they are very small so not many places for the driver to stop and get a good look of the view. I was fortunate that we were held up by construction near the top so had a chance to look around. Otherwise, I would basically had only very quick glances.
If you have a SRW truck, my suggestion would be to take your truck and if he doesn't see enough, may decide you want to take a Red bus.
