For non-modal/auxiliary verb, is the non-3rd person singular present form always the same as the base form?

The Penn Treebank Parts of Speech tag set differentiated between the base form of verbs (VB), and the non-3rd person singular present form (VBP).

Consider the following cases, with the different uses of rise:

base form: The share price will rise.

non-3rd person singular present: The share prices rise.

In both cases the forms are the same.

All the examples I have seen of verbs where that is not true, are with verbs that can be considered (by some definition) to be modal and/or auxiliary. Such as: be, am, are, is, was, were, being, can, could, do, did, does, doing, have, had, has, having, may, might, must, shall, should, will, or would

Are there examples of words from outside my modal/auxiliary list, of non-3rd person singular present forms that are different from their base forms?

I would particularly appreciate referenced answers, sourcing any statements about their nonexistence/rarity.

The answer to the OP's question is: 'yes'. Mostly. The only English verb which differs from its plain form outside of the third person, is the verb BE. The verb BE is usually an auxiliary verb.

However, the verb BE can also be regarded as a lexical verb in sentences such as:

• If you don't be careful ...

Notice that the sentence above uses DO as a dummy auxiliary even though BE is present. Because of this there might possibly be cases where it is impossible to distinguish between BE as a lexical or auxiliary verb. However, I know of no such cases. Lexical BE rarely if ever rears it's head as a tensed verb. Arguably the positive polarity version of the phrase above is:

• If you be careful

Here we are still using the plain form of the verb, not the present tense. There is a strong case therefore that tensed BE is always an auxiliary. This would mean that there are no exceptions to this rule.

However, there is one more issue that might put a spanner in the works here. The verbs BEWARE and USED have no present tense form in current usage. BEWARE is only ever used in the plain form because it only occurs in imperative constructions. The verb USED as in I used to smoke, is only used in the past tense. It could be argued, therefore, that these verbs do not have any present tense form that is identical to the base or plain form.

You can read more about lexical versus auxiliary BE in the reference grammar The Cambridge Grammar of the English Language by Huddleston & Pullum, 2002.