Take a look at the sentence again:
While Patrick is sightseeing, Squeeze will either
find a patch of sunlight under a window
or he will curl
up under a table lamp.
When you use either ... or, you must have two equal grammatical items. After either, notice that you have half a verb phrase, find [Will find is the whole verb phrase]. But after or, you have a main clause, he will curl up under a table lamp. The structure is not parallel.
To fix the sentence, you can change he will curl to curl.