Ok teach me something, how will knowing the exact reason why an old appliance is tripping a GFCI add to safety?
My SOP is if an appliance keeps tripping a GFCI I recommend disposal or professional repair of it. To me that is as safe as it can get.
A recent example, about a year ago a supermarket had a brand new commercial grade vegetable juicer that from the first time it was plugged in would trip the GFCI when switched on. This would be immediate and consistent. If I moved the unit to another location without a GFCI it would run fine. They asked me to remove the GFCI protection, I refused to do so and recommended they return the unit. Later I found out they had someone else remove the GFCI.
Fast forward to another supermarket chain who bought the same brand unit and it also would not run on a GFCI. Here is the difference though, this chain did contact the vendor of the machine and the vendor said 'Yes, we know that is an issue, we will send out a board'. One of our other guys installed the new board and the tripping stopped.
My point is that knowing the precise cause was not important, knowing that the unit was the issue and not the GFCI was what was important to safety.
Now if you want to go more in depth for your own curiosity and education more power to you but please don't try say safety will be greater for it as far as the issue we are discussing.