Yes that would be the primary way to locate. Unlike other parts of their military capabilities, their Electronic Warfare capabilities are actually very capable.
If you know the operating frequencies of a radar system its extremely easy to track a radiating platform. There are ways to mitigate being located. However, in the end every time you radiate especially with a radar system as powerful as these systems use, you are literally a massive beacon in the dark. Any attempt to mask this signature will likely degrade the capability of the radar itself.
What I think Russia are doing with these extended attacks is to force Ukraine to radiate these platforms for long periods of time, they will likely only turn them on at last safe moment when there is intelligence to suggest an incoming attack, hence you see all the NATO air assets up prior to attacks. In doing this they will be able to accurately identify the location of the tracking radars. One way to get around this is by radiating for very short periods of time bewteen multiple systems, its a method we call blinking. Its really only going to be effective on a mobile system though. and from what I've seen I dont think Patriot is very mobile.
One other potential way of locating these Patriot battery's is through HUMINT, people/agents on the ground physically locating the equipment. Though I think this is a lot more difficult and risky these days, may have been easier prior to the full scale invasion, not nearly as easy these days.
