I've been working with and in Japanese off and on since about 1988, but I'm not a native speaker, so take this with a grain of salt. :)
How to parse 店は人の多いところがいいです
人の多いところ
My understanding is that の marks the subject of the adjective 多い, which can be replaced が for emphasis...
Overall, it means "A place with lots of people."
Your parsing so far is correct.
Can 店は人の多いところがいいです be ambiguous?
I don't think so.
You point out:
ところ means "place" but it can also be used to refer to a point in time.
The term ところ used to refer to a point in time is, I think, always usually in the context of a verb phrase:
- するところ → just about to do
- しているところ → in the moment of doing
- したところ → just finished doing
I don't think it refers to time with most adjectives, where instead it refers to an aspect of something (as in 「彼女【かのじょ】のいい[と]{●}[こ]{●}[ろ]{●}」 "the good aspects of [my] girlfriend"), or to a location (as in 「蚊【か】のいない[と]{●}[こ]{●}[ろ]{●}」 "a place without mosquitoes", or 「カバの少【すく】ない[と]{●}[こ]{●}[ろ]{●}」 "a place with few hippos").
Can the above sentence convey the meaning "It's good when the shop is crowded"?
I don't think so. To convey the sense of "the point or span in time when a quality is present", I'm much more accustomed to seeing the word とき used instead:
店【みせ】は人【ひと】の多【おお】い[と]{●}[き]{●}がいいです
(Albeit, this isn't "crowded" so much as just "there are a lot of people".)
Addendum
As pointed out by @Nameless in the comment to this post, there are sometimes cases where [ADJ]+ところ
refers to a moment or time, such as 「忙【いそが】しい[と]{●}[き]{●}」 "a busy moment".
I think the reason that doesn't work here with 店【みせ】 and 人【ひと】の多【おお】いところ is because a 店【みせ】 is inherently a "location", as noted by @A.Ellett in the comment on the question, so ところ in context must mean a place. Meanwhile, because neither a person nor a person's current state is a "location", 忙しいところ cannot refer to a "busy place" and still make sense in that context.