Everyone makes the assumption that a quartz watch needs a battery when it stops. Usually that's the case, but eventually the movement reaches a stage where the lubricant has gone sticky and the current needed to allow the movement to run is higher than the battery can supply, it's like pushing a stone up hill and rolling it down the other side, if you don`t quite make the summit it rolls back. Each pulse of the movement is like that, the friction has to be overcome for the watch to 'tick' each second. Stripping, cleaning and re-oiling will usually get the watch running properly for several more years, but sometimes the circuit develops a fault and if that's the case the movement needs replacing. Swapping batteries on these ETA movements requires care, the coil has no protection and if it gets touched with a metal tool it'll fail.
ETA 955.112 movements used to be cheap and readily available so it made more sense to fit a new one if the watch developed a fault. I don't know what availability is like thesedays but most ETA movements are getting harder to source. Cousins used to sell loosepacked movements but I'm wary of these and I don`t trust the lubrication or cleanliness, I`d always want to strip one down and service it before trusting it. Movements in sealed packaging are far better but dearer and harder to source.
I`m not offering to get involved with this one at the moment, too many other things going on, but as I`ve outlined they can usually be fixed fairly easily. They're fiddly things to work on but not difficult, the risk of damaging the coil is the biggest headache.