You might take off the LNB cover ( the small trash can in your last picture above) and give us some pictures inside.
Be careful of any wasps, or other resident bugs.
Look also directly into the open end of the feed horn (as viewed from the dish), and let us see which model/brand you have (and any more critters).
There may be a two or three inch removable cover.
Let's see inside.
We'll be able to tell you if it'll do Ku, too.
Are you getting any old Analog or 4DTV receiver with the dish?
Perhaps a 920 or 922 4DTV receiver?
Reason I ask, is any of the above will move the motor to swing the dish.
Lacking one of those, we might recommend a thing called a Vbox or a Gbox to do the job.
Also, the feedhorn most likely has a little blue servo to change skew and switch between horizontal and vertical transponders.
An analog or 4DTV receiver would be able to control that servo, too.
There is a new product coming from Sadoun in about a month which combines the Gbox and Servo control, but we haven't seen the first unit yet.
Another solution would be to replace the feedhorn (all the hardware in that LNB cover above) with one that's voltage controlled for Vertical/Horizontal switching.
Your Coolsat will handle that task just fine.
However, it's way too early to be making any such suggestions into recommendations.
Let's see what you've got. What you want. And what you can get, hardware wise.