How can I attach the air cylinder to the tab and to the mount blocks? While not losing the ability to actuate the air cylinder and still making the head rotate.
In general, to close such "kinematic loops", you define multiple mechanism connections in the linking component.
It is not clear from your screenshot what the connections are - I will assume that your cylinder assembly ("6471K...") contains the bent sheetmetal mount "tabs", and that the component "HEAD_2_CYL" is the hockey-stick shaped connector that it is rigidly attached to the rotating "HEAD".
If that's the case, then edit the definition of the "6471K" component and:
1) add a connection of type "Rigid" where you constrain the cylinder's tab to the mount block.
2) add a 2nd connection of type "cylinder" where you constrain the cylinder's clevis pin to coincide with the hole in the HEAD_2_CYL component.