There are many answers already, but here'a a fun way to find them:
we can use the combined power of
hypercubes and sudoku.
This grid represents the 4D hypercube formed by the possible options. Position of switch 1 corresponds to the column inside a 3x3 box, switch 2 is the row inside a box, switch 3 corresponds to the columns of boxes themselves (we might call them "hypercolumns"), and switch 4 selects among the (hyper-)rows of boxes.
To cover all the possible opening combinations, we must of course test every switch pair in all their combinations. To make our plan as efficient as possible, we'll want to never guess the same position combination for any pair of switches twice, if it can be avoided.
This means we'd like to place our guesses on the hypercube so that no two guesses are in the same orthogonal plane along the cardinal directions. There's no prior guarantee that this is possible, but if it turns out to be, it will certainly be optimal.
For clarity's sake, the four cardinal directions of our hypercube are
- vertically inside a box
- horizontally inside a box
- to the same position in another box in the same column, and
- to the same position in another box on the same row,
and the 6 orthogonal plane orientations are those where the coordinates in exactly two of those directions are held constant.
Here's what it looks like if we highlight all the orthogonal planes that go through "row 2, column 2", which is more properly called "row 2, column 2, hyper-row 1, hyper-column 1", or even more to the point, "switch combination Middle, Middle, High, High".
The shape in the middle is the combination of the six, and corresponds to the set of all four-switch guesses that would duplicate an already-guessed combination for some pair of switches, which is exactly what we want to avoid.
Armed with all this, then, we notice that optimally placing our guesses happens to correspond to placing occurrences of a digit on a sudoku grid under a slightly modified "disjoint groups" restriction. That is, the digit must occur exactly once in
- every row,
- every column,
- every 3x3 box, and
- in every possible position inside a 3x3 box,
and the necessary modifications to account for the two missing plane orientations in 4D are
- no boxes that share a column may have the digit on the same row inside them.
- no boxes that share a row may have the digit in the same column inside them.
Well, then, let's just solve it! Since we have no fixed digits in the grid, this has quite a few possible solutions. Let's just pick the first one we come across:
And now we can just read the coordinates of the selected boxes to get an answer. (Reading the coordinates in any order is fine, as long as it's the same order every time. I'll start at the top and go counterclockwise, which is the same order I chose at the beginning.)
And there we have it: a set of four-switch guesses that includes every position combination for all possible pairs of switches (so it's guaranteed to work) exactly once (so it's optimal).
Epilogue: Even though a set of guesses is an optimal solution to this puzzle if and only if it fulfils the criteria given above, I fully support OP's choice not to include the four-dimensional sudoku tags, surely those would have been a dead giveaway :-)
Editor's note: this still reads a bit messy, as I made everything up as I went along. I tried to polish the answer a bit after a night's sleep, but there's still quite a lot to improve in terms of making the narrative easier to follow. I'm afraid the next improvement would require dropping the hypercubes out of the argument entirely, the reasoning should work without them just fine, but since that was the route my brain decided to take to reach the sudoku idea, (and also because hypercubes are way too cool to be treated like that), I don't think I'll want to make that edit after all. Sorry about that :-)