I followed this same algorithm as well. But in order to make an easy tool to find places to target, I created a scoring system by multplying the column and row number and the last dimension was the distance from the bulb. The bulb was a value of 7, the next square in a thermometer was a 6 and so on.
The scoring system wasn’t truly deterministic, but it created a colored heatmap of where I should apply my rules for ruling specific square in or out.
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I had a bit of trouble with it at the beginning until I threw it in photoshop and used it to clean up my work and figured a clean way to mark trial and error. Once I had that and marked off any spaces that couldn’t be it, I found a lot of information through trying out every solution for one of the rows that only had 1 space. It went pretty quick from there.