I had the same issue last year. The rod wasn't sliding as designed, causing the flush valve to open as soon as the pedal was depressed at all. I pulled the toilet and replaced the water control valve that was catching the rod. Simply lubricating it may have solved the problem but since I had the part, I changed it and cleaned and lubricated the old one for a spare. While I had it out, I replaced the flush ball seal at the same time.
While the part description didn't say so, it was packaged with a new floor seal, so you may not need to order that separately. Got the part on Amazon for about $20.
Not as bad of a job as I had imagined.
