One way to find out whether a verb appears in two homophonous forms, with and without an 'implicit argument', or, on the contrary, the two homophonous forms correspond to different lexemes (= different homophonous verbs) and there are not any 'implicit arguments' involved, is to use the 'zeugma tests', and the easiest to apply in cases like the one you cite is (rightwards= R) 'R-gapping' [recall that leftwards 'gapping', L-gapping, is disallowed in SVO languages like English] subsequent to coordination - under the assumption that the R-gapped coordinate clause will only sound natural, rather than like a pun, when the omitted second verb is the same verb that occurs as an antecedent in the first coordinate clause and thereby licenses 'R-gapping'.
In the case of the verb(s) give, then, if you coordinate two clauses like He gives blood and His wife gives to charity and try to 'R-gap' the second token of give, the result, He gives blood and his wife __ to charity, is obviously zeugmatic (i.e., either unnatural, or interpretable only as a joke, with the structure [He [gives [blood and his wife](= DO) to charity]]), which suggests that the two tokens of give that appear in those two clauses belong to different lexemes (= different homonymous verbs give1 and give 2), not that the first token of give is used with an 'implicit argument'.
Much the same happens with (dictionary)'verbs' like drink that can apparently be used either intransitively (= 'with an implicit argument?'), as in He drinks (daily/too much), or transitively, as in He drinks only beer. In this case, the difference in meaning is more notorious, which points to the existence of two different lexemes (= two homophonous verbs drink1 and drink2), but let's apply a couple of 'zeugma tests' anyway and see whether the results corroborate that intuition.
If we apply coordination followed by 'coordination reduction' (= CR), we get * He drinks daily/too much and __ ___ only beer, which is obviously zeugmatic (and plainly ungrammatical in this case). [Of course, we can save the construction by inserting a comma after the first coordinate, as in He drinks too much , and only beer, but that is no longer the coordination + CR test we are talking about here, but the addition of a parenthetic coordinate, which obeys rather different rules].
If we, instead, choose two parallel clauses with different subjects (say He drinks daily/too much and His wife drinks only beer) in order to be able to apply coordination followed by 'R-gapping', the result is * He drinks daily/too much and his wife __ only beer, which, again, is ungrammatical. Thus, in the case of drink, too, we should not say that the verb is used 'with an implicit argument' when intransitive; we must say that our lexicon contains at least two different homophonous lexemes, drink1 and drink2, with considerable differences in meaning and syntactic behaviour.
Those are, perhaps, the simplest 'zeugma tests' lexicologists can use to determine whether any two tokens of a given 'form' are manifestations of the same lexeme or not, but there are other such tests, applicable to verbs as well as nouns (e.g., modification by adjuncts that may selectively apply to different 'facets' of a lexical concept represented by a unique phonetic-orthographic form). It would be too long to illustrate them all here, and it would lead us away from your question, but if you apply such tests in a systematic way, in principle you should always be able to decide whether an apparently unique 'verb' alternatively takes an argument explicitly and implicitly or, on the contrary, what happens is that the English lexicon contains two (or more) homophonous verbs with different adicity and more or less prominent differences in meaning.