As an old school DM, I would allow a telekinesis spell or telekinesis feat/ability to be used to try to pull or push a person from the interior of a gelatinous cube. To me, this would be similar to using the same spell or ability on a person or object in relatively clear water or air (clear enough to see the person or object). All of these substances are transparent or translucent fluids or gels. You could even try to use the telekinesis spell/ability on someone encased in a block of ice or glass, but the spell would move the whole block unless you could crack it open so that the person could be moved separately. As a corollary to this line of thought, you cannot apply telekinesis to an invisible creature or object because you can not see them.
To me, “total cover” means that someone is obscured or hidden (e.g., a person has “taken cover” or is hidden around a corner or behind a table, etc. As a result, the constraint on being able to view the target would be violated. This is all about vision being necessary to focus the ability.
If a person were submerged in a mud pit, then telekinesis would not work. If there was a hand or arm visible, even if covered in mud, then it would serve as an appropriate focus for telekinesis. But the telekinetic force would be applied to the visible part, at least until more of the person or object was revealed. So, if a person’s head was the only part visible, you would initially be dragging them out of the mud by their head (ouch, neck damage!)
Consider another case - a fighter totally encased in plate armor or a person fully wrapped on a big robe - with no visible flesh or features. In the spirit of the spell/ability, you can discern the person because the armor or clothing is “connected” to them. The mud covering an outstretched arm would be treated similarly, since you can discern the protruding arm coated by the mud. You could not fish around in the mud to find a person or object because there would be no visible feature to focus the spell/ability.
Don’t take the fun out of the game! Encourage creativity. AD&D was never meant to be hidebound to the rules.
P.S. In my opinion, the saving throw in the example would be rolled by the gelatinous cube attempting to hold onto its prey. The person isn’t resisting the spell/ability, but the cube is.