This is absurd though. First of all, you're assuming Employer B knows about the other job, but they don't have to. There's asymmetric information (and one of those interesting cases where it's actually the worker who knows more than the firm). So as long as the worker doesn't allow the firm to know he's doing overtime, your entire argument falls apart.

But there's more problems. You're also acting like Employer B knows the wage of Employer A and is basing their entire wage decision based on that other company's wage. But that's ridiculous. Employer B sets a wage that works for their costs and what the worker can produce for them.

You're also assuming Employer B knows the other wage and will just lower their offering wage just to spite the worker because they can. But no business would do this. And they don't have to compete with Employer A's wage any more but they sure do have to compete with the wages of Employer C, D, and all the other firms in the market. If they offer such a low wage the worker can go to the next business over and work there.

Your also acting like the worker would accept this lower wage, but people have reservation wages, which usually increase as there are more hours worked. That's the whole reason most places pay extra for overtime. If they're offered a substantially lower wage for extra work above 40 hours, they would just not take it.

So in order for wages to reduce, we would have to assume: Employers know workers are using them for overtime work, know the worker's current wage, throw their set wages out the window and construct a completely new lower wage, and are able to do this because they don't have to compete with one single firm (and somehow no other firm exists), and a large portion of workers must be so desperate for cash that they are willing to work for lower wages the more hours they work.

I don't think you will find evidence to back up this hypothesis.