Check all of your fuel line connections, especially filter, fuel pump and carbs and tank.
Some TR-6 models had a charcoal canister and the fuel system was sealed, e.g. no venting. Could be this system needs service.
It is not uncommon for small pin hole leaks to develop in the gas tank, especially where it sits on top of the ledge in front of the boot. These leaks start with rust due to trapped moisture. You can easily inspect the possibility of a leak by removing the mill board cover behind the tank (inside the boot).
There is a small length of rubber hose which connects the fuel cap outlet to the tank. Make sure that the rubber has not deteriorated and started to leak.
I'm sure others will have additional suggestions.