Well, the third person singular of the present tense (indicative) of all verbs except the modals does end in -(e)s, and is indeed always finite, but I am not sure that your way of determining whether a verb is finite is particularly helpful. See, for example, the following sentences, in which the underlined verbs are finite:
I am working hard at the moment.
Stand up, please.
Will you pass me the salt, please?
If that be the case, we might have a problem.
I inisisted that he leave immediately.
Student or Learner