I have ridden the Pig Trail several times on a motorcycle
Based on my experience, there is only one curve that could be a potential problem... it's a pretty tight hairpin curve pretty close to Turner's Bend (you should stop at Turner's Bend... very cool little general store there).
Anyway, in a 31', I don't think you will have any problems. And, on a Monday, the traffic will probably be lighter than on weekends.
If you are traveling from the north to south, you can actually look down to your left and see if there is any traffic coming from the other direction, before you go into the hairpin curve.