I think you are taking too much into your own hands.
You are working there, and you require adequately clean facilities for your comfort, and the company is failing to provide them.
Go to your manager and complain. "The bathroom is consistently dirty, daily."
If they don't address the issue in a way that resolves the problem - regardless of the cause - then go to HR. "the bathroom is consistently dirty, daily."
They are responsible for providing clean facilities. It's not your job to investigate, provide evidence, or find the root cause. If they choose to do that, that's fine. If they choose to get a cleaning service (or an employee) to check and clean the toilets more frequently, that's fine.
If they don't resolve the problem, then you may be able to file complaints with your local governments about conditions of employment, but unless body fluids and other excrement are placed in areas you are expected to come into direct contact with (ie, outside the bowl), then it's unlikely that you will receive any relief. You may need to find another job, or put up with unpleasant scents and sights wif they pose no actual harm to your body. Perhaps a bathroom scent dispenser may resolve some of your concerns.
Regardless, I'd strongly suggest you drop all concern over who is making the mess, and only concern yourself with how the mess is affecting you, and conveying that concern to the people who are in a position to resolve it.
If you bring up the individual, or the sex of the individual, they may view it as a problem between two employees, or a personal bias on your part against men. This is not what you want them to focus on - at least not if you want them to take action on the messiness left behind.