As you surmised, this is covered in Total Warfare, starting on p.151.
Provided the hex the target 'Mech was displaced in to is at least 2 levels lower than the level of the hex is started in, a fall automatically occurs. You would resolve such a fall using the difference in elevation.
Normally, a fall would be ('Mech's tonnage / 10), in this case, it would be ('Mech's tonnage / 10) * 3. 1 because it's a 'Mech, +2 because of the 2 level elevation. Damage would have been 'times 4' if it was pushed from a Level 3 hill in to a Level 0 hex.
Possibly a handy tip: you may want to look in to the Death From Above and Charge attacks as well. DFAs can be quite useful in knocking someone off a hill.