I beat the game with 6 man team.

Thinking of doing a run with just 2.

Cleric and what else?

I played a semi-cheated 2 man team on the vanilla TOEE without Fragarach/Scather.

One full cleric, purely for item creation feats, and a paladin/rogue/monk/fighter for death and destruction.

Semi-cheated by giving both characters 18's across all stats, but otherwise played and beat the vanilla campaign without any other intervention. It was challenging in the beginning but by the time I reached the temple my main pal/rog/mon/fig was way overpowered.

The key to success for my build was having great cleave with dual wielding great cleavers with improved crit (handaxe), producing a threat range of 13-20. Second key was saving Prince Thrommel as soon as possible before exploring the temple in order to get adequate money to make worthwhile magic items early. But that secret room with 3 wizards and 20 men you have to go through on the way to Prince Thrommel was probably the hardest part of the run. The Balor was a slight challenge and Zugg was cake. I even managed to kill Iuz, though I had to try about a dozen times to kill him before the 3 round limit.

It might be possible without starting off with all 18 stats but I don't have the patience for that.

By 2-man team I assume you are not going to use any NPC slots? In that case, any build that allows you to cast Charm Person. I recommend a Wizard 1/ Bard. See the thread in his forum "How to Bard". Having both a cleric and a Wizard will eventually allow you to forge any magic item available in game (or enhance existing ones), which will help quite a bit.

That would be pretty tough, since when no slots are occupied by "living" PCs, the game activates the "you lose" screen.

You could, however, try beating the game using only a single PC that has 3s in all 6 attributes.

The question is, of course, when does the game check to see if there are no living PCs? In particular, is there some way of tricking the game into letting you have no living PCs, but still play? If so, how much can you do without triggereng the "you lose" screen?

I can think of a few games where that is possible. Bard's Tale 3, for example, will let you drop the last living character if it's a monster or illusion, and won't give you game over until after an enemy attacks (who does the enemy attack?) or you step on a damage square. Final Fantasy 5 and 6 both have situations where you can have an all-dead party outside of combat, and the game won't end until you get into combat (and Phoenix Downs can be used from the menu since items used that way aren't used by a specific character); FF6 provides a way to get an empty party (when Shadow alone arrives at Narshe, he leaves your party, leaving you with nobody), though the game unfortunately softlocks at that point. I remember in Might and Magic: World of Xeen getting a party where the only PC was petrified; one move would end the game, but I could in theory save the game in this state.

Edit: I could also mention Dragon Warrior 3 (NES), where it is possible to have an all-dead party, and if you do, the game misbehaves and corrupts memory; this has been used in a speedrun to skip most of the game, including one particular major boss.