Hi and welcome,
You've gotten a lot of good suggestions. I can only add a couple things that I don't think anyone has mentioned:
1. Depending on how old they are, all the rubber fuel lines might need to be replaced. Older type rubber is attacked and damaged by modern unleaded fuel formulations. This can lead to leaks and/or fouling of the carbs if small, gummy particles break off the inside of the hose and travel through the system. Modern rubber lines are widely and easily available at auto parts stores, or through your mechanic.
2. The fuel tank is vented. On TR4 it's on the RH side, I'm not sure about TR3. On TR4, a vent tube goes from the RH top of the tank, down the side and out through the floor of the car. This vent is necessary to allow air into the tank when running the car, or a vacuum would form and effect fuel flow in the relatively low pressure system. Check that the vent is all the way out through the floor of the car, usually terminating just above the rear axle. I've seen these vent tubes get damaged by vibration and broken off short, ending up dumping small amounts of fuel into the trunk area where you certainly will smell it and don't want it.
Leaking oil is not all that uncommon with LBCs. In fact, some say it's part of the cars' charm! However, depending upon how much and where it's coming from, there might be a few things you should check. There is a breather tube on the LH/rear side of the engine. If there is a lot of "blow-by" past the piston rings, as a result of wear, the vent tube can see more than usual amount of oil mist being pushed out. This situation might improve in time, with a car that's been stored for a while. But, it can also be an indication the engine is getting a bit tired and might benefit from a rebuild soon. Over-filling the engine oil can also lead to more than usual amounts of oil being pushed out the breahter tube. The original "scroll-type" rear main seal on the engine is another common source of leaks, but actually works pretty well if installed correctly. Leaks from the valve cover, front engine cover, oil sump pans and rear differential cover are most often caused by overtightening their fastening nuts and bolts. That warps the covers to the point they won't seal. The solution is just to remove them and do a little work on the flanges to re-flatten them, then reinstall bieng careful not to overtightening. I like to use Hylomar on many of these seals, it's good stuff.
The rear axle and gearbox can both start leaking if their vents get plugged. What happens is the oil and air inside the gearbox or diff heats up during driving, and expands. If there is no venting, oil can get pushed past the seals. Sometimes it's just a matter of cleaning the vent area (being careful not to drop anything inside). Other times various seals need replacement, too.
Part of the "aura" of these older cars is a lot more odors of oil and gasoline than with modern cars. It's sort of surprising how much, if used to driving only late model cars. So the trick is to tell the difference between "normal" aromas and abnormal ones! I think it's safe to say that if the smell of gasoline from the garage is permeating your house even after 24 hours, that's a lot more than normal! You are wise to have the mechanic look at it and help. Could be a serious safety issue.
Let us know what your or your mechanic find.
Enjoy your Dad's old car! Some years ago my Dad gave me his old Leica cameras and lenses. You can be sure I'll never part with them!
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