The following is based on Chanting the Hebrew Bible by Joshua Jacobson (as well as experience leining, but note that my experience is with American and British leining; other Ashkenazim might have other minhagim).
The only time the munach gets the shaky trope is when it's a munach-legarmei, which visually looks like a munach followed by a psik. The munach-legarmei is a "טעם מפסיק" (a disjunctive trope), whereas the normal munach is a "טעם משרת" (a conjunctive trope), so it makes sense to give the shaky trope only to the munach-legarmei. See any tikkun for a list of disjunctive and conjunctive tropes.
However, there are instances where a psik (ie. a vertical line) follows a normal munach, and it is not a munach-legarmei (eg. Ruth 1:13). Except for the exceptions noted below, the rule is as follows: munach-legarmei must be followed by munach revia (occasionally, another munach-legarmei, or a geresh or darga will be in between the munach-legarmei and its munach revia); all other cases are a normal munach followed by a psik.
Exceptions: Lev 10:6, Lev 21:10, and Ruth 1:2. In place of a telisha-qetana before geresh (yet still a disjunctive): Gen 28:9, 1 Sam 14:3 (second one), 1 Sam 14:47, 2 Sam 13:32, 2 Kings 18:17, Isa 36:2, Jer 4:19, Jer 38:11, Jer 40:11, Ezek 9:2, Hag 2:12, and 2 Chron 26:15. R. Breuer's Ta'amei HaMiqra adds the following, before pazer: Neh 8:7 and Dan 3:2.
A word on the exceptions: in Lev 10:6, Lev 21:10, and Ruth 1:2, the munach is preceded by a mercha, which is not normal for the pashta which follow (we'd expect another munach), but is normal for a munach-legarmei. In Isa 36:2, the munach should be a telisha-qetana, and so it's not a normal munach (although it is a "puzzling exception in that the conjunctive appears to be munach", says Jacobson). [Jacobson's puzzle is quickly resolved upon seeing that unlike the Leningrad Codex linked to before, the Aleppo Codex has the expected mercha.] In the second set of exceptions, we expect a telisha-qetana, and thus what we have must be what Jacobson calls an upgrade (where a normally conjunctive ta'am gets replaced by a disjunctive one), and so it is munach-legarmei. In addition, in 2 Kings 18:17, we see the expected conjunctive mercha before the munach-legarmei. In Neh 8:7, we have the expected mercha. In Dan 3:2, however, it seems like it could go either way (as munach is the normal conjunctive of pazer). Jacobson quotes Breuer's Ta'amei HaMiqra, Heidenheim's Sefer Mishpetei HaTe'amim, and Perlman's HaMesorah.
As to your examples:
munach munach pazer -- will always be normal munachs, except possibly in the two exceptions listed above, Neh 8:7 and Dan 3:2.
mapach pashta munach munach zakef-qaton & munach zarka munach munach segol -- both munachs are normal munachs, and sound identical, ie. each the same as if there were only one munach there.
mercha munach etnachta -- does not appear in Chumash; perhaps you meant tipcha munach etnachta, whereupon in this case also the munach would be a normal munach.
The only place I've seen where other people (not I) do a shaky trope on a munach that isn't a munach-legarmei is: munach mapach pashta zakef-qaton, and similar. I believe (and it seems that Joshua Jacobson also believes) that this would incorrect, as this munach is a conjunctive trope, and should lead in to the mapach which leads in to the pashta, instead of standing on its own.
As @DoubleAA points out, Rabbi Breuer holds that in the phrase munach | revia, the vertical line always indicates that the munach is actually munach-legarmei, contrary to the opinion(s) quoted in Jacobson's Chanting the Hebrew Bible (except in Isaiah 42:5, where the mesorah ketana indicates otherwise). The mesorah ketana substantiates this position, by indicates at Isaiah 42:5 that there is the only occurrence of this pattern with a psik (and not a munach-legarmei).