You should be able to leave to a neighboring country for a 2 or 3 nights and just re-enter Thailand for another 60 days..
The only thing I would say is don't expect to just keep doing that several times consecutively as at some point in the future the Thailand immigration may question you about being a genuine tourist and could refuse entry if they believe you are trying to live in Thailand on just tourist excemption entries.
When it's finally implemented it's going to be an app or website for you to advise Thailand immigration of your visit in the near future..
Name, passport number, dates etc ....
Countries like Singapore and the Philippines already have an ETA in place so it's not a new idea..
The USA has had a similar system in place for years for foreign visitors..
It's a way to screen visitors before they arrive and reduce the number of turn backs at the border who may have criminal records or overstay history in Thailand...
If your ETA isn't approved then don't bother going to Thailand and the airlines are likely to check ETA approval before you board the flight.