Maybe your path contains special characters, try using match and just specifying part of your path to see if that works. If that's the case then try replacing the match with the "==" and escaping the special characters with a backslash. I would also include a default condition (1==1) in case none of the others match and also create a variable with a different name (like NewPath) to avoid overwriting your Path variable while you are still testing this and in order to see what's going on:
mysearch
| eval NewPath = case(
match(Path,"my path") AND Action=="check", "Yours is available",
match(Path,"your path") AND Action=="didnotcheck", "Mine is available"
1 == 1, "Others"
)
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