Much of Route 66 is not accessible to big rig trucks. Some portions are maintained by private funds (i.e. not tax dollars.)
Stopping on Route 66 is often free of big trucks, however, check and make sure you leave plenty of room for traffic to pass. Even if you feel like you are in the middle of nowhere, a speeding car can come along at any time.
As you can see by the above photo, there is a pull-out area. The road is decent, but it does have a lot of cracks, and it is windy in this area. (Some areas are flat and straight, others windy and mountainous like above.)
When taking photos roadside, be careful! Shooting during daylight is safer than shooting at night. At night, park where you cannot be rear-ended! During the day, give plenty of room for traffic.
If you go out in the road to shoot, have a spotter. The spotter’s job is to watch for traffic, both ways. They should yell to you to move to the side of the road.
Wear bright colors. Grays and browns blend in to the background. At night, wear something reflective, like a safety vest.
Speaking of Truckers
Here is a group covering Route 66 – The Blues Truckers. The rendition is good, and it has a nice slide show to accompany it.