I was wondering how were the dirt roads leading to the tram,and places to offroad and camp? Maybe do an expedition there one or two days with some folks from the portal.
On my most recent trip the roads were quite good. The previous snow drifts were gone and the road was undamaged by mud. There are two sections that require 4WD. One is between Cerro Gordo and the Tram cabin. Coming from Cerro Gordo (Keeler entry) it is a loose left-turning uphill section with lots of ruts. The other is the section coming from the other side of the Tram Cabin (Swansea entry). It is a loose dirt uphill section followed by a steep and rocky uphill section.
Modest ground clearance is fine but vehicles with a wide stance will have to beware of tire sidewall damage.
As for car-camping there are a few places but it is so limited due to all of the so-called "wilderness" road closures.
Coming up from Swansea has the best areas:
After the uphill rocky section there are a number of nice sites in the trees above 6500 feet. After that you could camp by the Burgess Mine cabin but if it is windy you are fully exposed. Great views in all directions! You can also stay in the old Burgess Cabin. It is often used by hikers of the Lonesome Miner Trail. The best spot is close to the Tram Cabin on the right side of the road on a little spur that provides great views of the Sierras.
Coming up from Keeler towards Cerro Gordo:
Before C-G there is a lot of "private" desert land (mining claims) that is not that suitable. After you go through C-G on the road towards the Tram Cabin there are a few spots but none are far from the road so any vehicle activity won't be far away.
In my other planning posts on the Tram there is a link to great topo map from a Land Rover club. Search on my name as author. Keywords are "saline", "salt', "tram" and "Inyos"