FWIW, Checking a 4-way switch

[Thatguy]

Label a switch terminal "1".
Find a terminal that has continuity to 1 and label it "2". Label the other two terminals 3 and 4 and check that they have continuity and
that there is no continuity between 1 & 3.

Flip the switch lever:
if there is now continuity between 1 and 3 there should also be between 2 & 4 and none between 1 & 2.
or
if there is now continuity between 1 and 4 there should also be between 2 & 3 and none between 1 & 2.

[hj]

Or look at the back of the switch to see which terminals are marked "Line 1" and which are "Line 2".

[Thatguy]

Or look at the back of the switch to see which terminals are marked "Line 1" and which are "Line 2".

From all the 4-way switch trouble people are having I thought the terminals were unlabelled and uncolored.