Assuming your PS2 has a network adapter handy (or a built-in one), you could potentially connect it via Ethernet to a Wi-Fi adapter or a PowerLine adapter.

I don't have any experience with either type of adapter, but I presume PowerLine would be more reliable than Wi-Fi since it's wired (uses your power plugs to route Ethernet data). However, it might be significantly more expensive and harder to setup.

If you go with a Wi-Fi adapter, I'd recommend ensuring you get a decent quality one that can get a strong signal. TMBO is prone to lag, so you wouldn't want to compound that with a poor quality Wi-Fi signal.

Good luck !


PS:
I'd recommend joining the TMA Discord server if you haven't already. All of the TMA's TMBO players hang around there.

I don't have any first-hand experience with Verizon. So I'm not sure. Maybe someone else might be in a better position to comment.

If your set-top box's Ethernet port is designed to provide network access to another connected device, it might be possible to connect your PS2 to it as a starting point to getting a working TMBO setup. But if that Ethernet port doesn't provide network access, you'd need to find another way of connecting your PS2 to your home network.

Once your PS2 is properly connected to your network, you'll need to do a few other things to be able to connect to the TMBO revival server. For more details, check out the TMBO Revival Server - One Year Later thread's OP and the TMBO revival server website's network setup page.

Btw if your ISP's modem/router hybrid blocks alternate DNS addresses, you might need to use cheat device codes to get around it.