I agree with johnlee that "waiting" in this sentence should be classified as a participle, not a gerund, if you are working in a framework that makes that distinction.
(Comments by members like BillJ correctly point out that not all frameworks do make this distinction; however, as far as I know, there is not yet a unanimous consensus in favor of the position that it is theoretically impossible to distinguish "gerunds" from "present participles" in English. You can see some relevant comments beneath the following Language Log post : Gerunds vs. participles.
The linguist Greg Lee made the following comments on this site about the post:
Liberman's post makes no sense to me. Because Liberman as a child couldn't tell the difference between gerund and participle, I'm supposed to assume they're the same? What kind of reasoning is that? – Greg Lee Dec 22 '16 at 5:11
I looked below in the comments at Stephen C. Carlson's summarizing the CGEL "argument". He says "OK, I've had a look at CGEL about abolishing the distinction between gerund and participle, and I have to admit that I didn't find the discussion particularly clear or persuasive." Based on his account, I agree with him. – Greg Lee Dec 22 '16 at 5:21
Also, see Araucaria's answer here: Difference between gerund and present participle. There is more complicated discussion beneath Greg Lee's answers to "Do these two sentences use the possessive case of gerunds properly?" and "How can you tell when a participle is being used as an adjective?")
I disagree with johnlee's statement that "A rule of thumb is that it's a present participle if it's used like a verb, or a gerund like a noun."
The salient characteristic of a participle is not that it is "used like a verb" but that it is a verb used like an adjective. (We wouldn't need any special word for a verb used as a verb.)
For example, in the progressive construction ("They are waiting"), the participle "waiting" is used after the copular verb be, similarly to how an adjective like "awake" occurs with the copular verb be when used predicatively: "They are awake".
To distinguish a participle from a gerund, therefore, you should try to figure out if the verb (or the phrase headed by the verb) is acting more like an adjective--in which case it is a participle--or more like a noun (more properly, according to some linguists, this would say "like a noun phrase")--in which case it is a gerund. (One point that may cause confusion: according to most systems of grammatical terminology for English, neither the term "gerund" nor the term "participle" is applicable if the word actually is a noun or an adjective—only if the word is a verb "acting as"/"used as" as noun or adjective. A noun ending in "-ing" may be categorized as a "gerundial noun" and an adjective ending in "-ing" may be categorized as a "(de)participial adjective", but these are not considered to be the same as gerunds and present participles.)
We can use adjectives after "while":
As far as I know, we can't use nouns after "while" in a similar fashion:
- *While sleep, people dream.
So it seems to me that "waiting" is not a gerund here, and therefore must be a participle.
(Specifically, the answer by Araucaria that I linked to earlier said that "In traditional grammar, a gerund is an -ing form of a verb that heads a phrase functioning as a: Subject of a clause - Object of a verb - Complement of a preposition". So it would only make sense to analyze "waiting" in "While waiting for service" as a gerund if you analyze "while" here as a preposition. I don't think it is.)
Another reason I feel like "waiting" is a participle here is because the sentence seems similar in meaning, and I think in structure, to sentences like "While patrons are waiting for service, they can enjoy coffee and snacks and mingle with their neighbors in need." In the preceding sentence, "waiting" is obviously a participle and not a gerund.