Hi,
I'm a mechanical Engineer from the Indian Institute of Technology Madras. I've read your project requirement, and I find it very interesting. I'd like to solve it.
Your problem has the additional challenge as it is designed for a cat, and not a human. So I like this challenge, and would like to solve this for you.
I already have a couple of designs in mind regarding methods to sense the cat coming, and methods of activating the toilet flush. I've worked with such sensors and actuators as part of course projects before. I'll ensure you do not need to modify your flush. You'll just need to stick some devices around it.
I'll design this such that it can be readily implemented by you. You'll not need any more help from anyone on this. I'll also keep you regularly updated through the time I'm working on the project, taking your feedback in every step so that we can design the best product.
Please reply so that we can discuss further. Awaiting your reply.