My mystery squash have bloomed! I had saved some seeds last year which I think where from a pumpkin but I am not sure. Planted them in a pot just to see what would happen and they grew! They don't seem to be making runners which I thought was common for pumpkins.
I thinned them twice already since I wasn't sure if they would grow (I just tossed some seeds in) and I still have five plants. Now the wait begins!