Help with vintage funky Eberhard watch

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Hello fellow forum members,

I got a cool looking vintage Eberhard & Co watch, I think from the 70’s.

I wanted to open up the case so I can take a look at the movement. However, it opens by pushing in two pins at both sides simultaneously. I tried it myself but with no luck. Does anyone know what tool I should use or can help me with opening it up?
I found one other example online on an Italian forum. Tried to contact the OP but no reply.

Thanks in advance.
Jan