What is the problem with your current arrangement? Does this hurt the pump in any way?
At the moment the pump runs all the time, when there is no need to as the tank just overflows. Wearing the pump out prematurely.
Ok, fair enough. But, you never said anything about that... or I missed it. But, you still did not answer the question. I will assume it does not harm the pump to run without moving water.
This is an easy problem to solve, depending on your level of experience with electronics. Restating your problem to: "I want my pump to only run when the tank is not full."
You will need a level sensor in the tank, which can be as simply as a float connected to a switch. I have seen these in cisterns and they are very common. I don't know if they handle the power line voltage, but I would want to use 12V power to be on the safe side.
So you need a 12V transformer to supply power. This runs through the tank switch to a relay. The relay switches the power to the pump. Now, the pump will not run unless the water level in the tank is not full.
If you don't want the pump to run when the solar level is too low, you will need a light sensor for that, which can operate another relay, wired so both need to close to provide power to the pump.
Is that clear enough?