A lilting litle melody, similar in tone to "Cloudy" or "Feelin' Groovy."
The imagery here is possibly drug-related, or -induced, which is hinted at by the tune whistled at the end: "When I Was High and Mighty."
That said, there are plenty of druggy songs that have nothing to do with breakfast. Even given that it is a psychedelic lyric, why this imagery?
The imagery seems to conflate the images of breakfast foods with being on the beach or poolside, "relaxing a while." The speaker wishes to "float" like a cornflake and "com[e] up brown," as if tanning, in the toaster.
Hollywood imagery is here, too. The cornflake would be "talking movies... living in style." The other character is a raisin (long before the Marvin Gaye-singing claymation ones of commercials) who "occasionally plays L.A." The two-word bridge, wafted in by Garfunkel, is simply "South California"... which is where Hollywood is, map-wise.
As the speaker notices the raisin's toupee, it seems the speaker longs for the easy pace of life in that part of the country... but not the obvious falseness of the social scene. As Oscar Levant famously quipped, "Behind the phony tinsel of Hollywood lies the real tinsel."
But this is not the speaker's reality. Not just the not-being-breakfast part, but not having the carefree life he imagines the food has. The first two lines of the first two verses are, "Wish I was..." Implication: "...but I am not." He is not relaxed or at ease.
Actually, he is the opposite-- he is at attention. The imagery abruptly shifts to reveal why the speaker wishes he was lounging in an LA pool; it seems he was drafted: "If I become a first lieutenant..."
As dire as this possibility is, the speaker is determinted to romanticize it, or at least be sarcastic about it. He imagines a spiffy portrait of himself ensconced "on the piano." The note on the photo seems more WWI than Vietnam, however, in tone and in name-choice; a simple, chaste "To Mary Jane-- Best wishes, Martin." ("Mary Jane," may, of course, be a reference to marijuana. That would explain the drugginess of the song, and the desire for food.)
Chances are, he would not fit in within the army structures and strictures. After all, he does not "prefer... ordinary jam." Rather, he likes the obscure, obtuse "boysenberry."
Anyway, this new idyll, of the soldier and his best gal a-missin' each other, is now broken, too. While he's away, a man who has cravenly decided not to serve his country is also cravenly having his way with this very gal! But the tone is still light-hearted, and the sound effects here are of "Roger, (the) draft dodger" not "tip-toein'" down the stairs discretely but stumbling down them loudly and clumsily. Now, "everybody knows" not only "what" he is after, but when he is after it.
Going back to the title, what is "Punky's Dilemma"? We don't know who Punky is, having only been introduced to Martin, Roger, and Mary Jane. But we can guess at his dilemma. If he goes to war, he is guaranteed that his girlfriend will not wait for him. But if he dodges the draft to stay with her, he ends up like Roger, sneaking around "the basement door," and having no kind of above-ground, above-board life.
How to decide? Bleary-eyed from a night of indecision (and other escapist pursuits?), poor Martin looks at his breakfast and longs for a simpler, more relaxed life free from war and potentially unfaithful girlfriends.
Maybe lying on a pool raft, like Benjamin in The Graduate.
Note: This song was covered by Barbra Streisand on her 1969 album What About Today?. She traditionally had performed older standards; this was an attempt to interpret works by the acclaimed composers of the day.
Next song: Mrs. Robinson