Improvise tool for lever lock? - eviltoast

I have an antique desk which has three locks and a single key.

My key continues to work for one of the locks, but when inserted into the other two lock key ways, the key will not turn in either direction (will basically wiggle a millimeter or so in either direction, but does not start to actually turn).

I am a very amateurish lock picker—I can rake a basic lock or use a snap gun, but this lever/mortise lock is very different from anything I have tried to pick before.

I should mention that I used the working lock to confirm that the key fully inserts into the other two locks before attempting to turn the key.

I’ve tried looking up tools for picking this lock and watched some YouTube videos.

I am curious if anyone with experience picking this sort of lock might offer some advice on tools to get or improvise.

I’m including a photo of the key to help identify what might be needed.

Any advice is appreciated.