From the upper end, any moderately high clearance vehicle can transverse the right-of-way down to the tunnel. Here or there may be a rock that needs to be moved, or a tight spot to navigate. About four years ago I took my Toyota Corolla down to the tunnel; the current one has some sporty flashing below the bumper that may affect the clearance.
I have not been up from the bottom in many years. Thirty or so years ago I took a Toyota Corolla (I'm on my fourth Corolla) to within 500 feet of the tunnel.
The big cuts appear to have sloughed in and would limit the access. From the present day highway it does appear that there might be vehicle tracks through the cuts. Now days, there does not seem to be any access to the grade from the lower end without going past the ranch buildings across the valley from the grade. The other approach to the bottom end could be to go down the old, old road to where it crosses the grade below the bottom fill. About 15-20 years ago I was in a friend's Four-runner and we drove up this old road after visiting the tunnel -- I don't know now passable this grade is now.
Brian