You are correct; if c1 does not have a common meaning between patients, then electrode designation is not really a meaningful variable and it's better to think of them as multiple equivalent measurements on the same subject. So your second model is more appropriate.

[More of a comment, left as an answer because I don't have enough reputation to comment]

You are correct; if c1 does not have a common meaning between patients, then electrode designation is not really a meaningful variable and it's better to think of them as multiple equivalent measurements on the same subject. So your second model is more appropriate.