Manual toilets are designed for raw water use only. There is NO SAFE WAY to connect a manual toilet to a potable water supply. Don't even think about doing it. If you want to flush with fresh water, add a dedicated tank that feeds only the toilet, and refill it as necessary.
Or, add a "Y" valve to the vanity sink drain in the head, with one output of the "Y" valve re-connected to the existing drain and the other output plumbed to the intake of the head. When you want to flush the head, turn the "Y" valve to feed the head, and run some water into the vanity sink. Then pump the manual head. When done, return the "Y" valve to the previous setting.
Also, with the "Y" valve method, you can leave the water in the sink after washing your hands, etc., then use that water later on to flush the toilet. So you can get additional use from the water before it goes overboard.