It is the Oscillator for the Control Valve. Not all tractors have this and it will work without it although. The "hole" under the PTO shaft is the Control Valve, treat it with respect.
There is a small circlip that holds it all together in the open end of the Control Valve, make sure that this clip locates properly or it will come apart again. Avoid touching the Control Valve polished outer surface as this will easily get marked and this could cause the Valve to stick. Never park the tractor with an implement in the raised position and with the Pump not running, as that can also cause the Control Valve to stick. There is no need to leave the implement in the raised position and it is dangerous too. I have attached a drawing of the Oscillator and Control Valve. There is a later type as well that is made of flat strip, but it does the same thing. If you have any problems with this, email me...John(UK)....firstname.lastname@example.org