Note that the smallest category of the response (samemate == 0) has
12 observations. According to a rule of thumb, you need 10
observations in each response category per parameter in the
model. Hence a model with one (if you're lucky two) parameters is
doable.
Complete separation appears when for a combination of covariates all
responses are 0 or 1. Adding complexity to the model, increases the
probability of complete separation because you have more possible
combination and a lower number of observations per
combination. Adding a random effect with 59 levels to a dataset of
66 observations guarantees complete separation...
The separation of the simple glm(samemate ~ success) is not that
bad. But glm(samemate ~ success + type) will give (quasi-)complete
separation. The glm model gives implicit warnings (see the last
model in your first email): type has a very large effect size and a
huge standard error.