The nouns spectrum and gamut both refer to a broad range of similar things arranged along a scale, but there are significant degrees of difference between them. The scientific meanings of spectrum carry over to its general usage, where emphasis is on the overlap and hence continuity between items on or along the spectrum. A spectrum is often contrasted with an either-or conception of something. In a spectrum of political beliefs, for example, liberals and conservatives are on the same continuum. Gamut, as suggested by the common phrase the whole gamut, emphasizes the comprehensiveness of a range and hence the variety or contrast encompassed by it: Love involves the whole gamut of emotions, from despair to joy. Of just about any set of wide-ranging and varied things (reactions to a movie, a dessert menu) we can say it runs (or covers or spans) the gamut.
The adjectives brief and fleeting describe things of short duration. Used of events, brief can simply mean lasting a short time: a brief period, a brief meeting, a brief hello. Applied to speech and writing, brief suggests concise and effective: a brief introduction, a brief summary. Fleeting is used of things that pass quickly, with the suggestion that they escape our grasp or are over too soon: the fleeting pleasures of youth, fleeting fame, a fleeting thought, a fleeting glimpse. Fleeting can imply a poetic poignancy, but also fickleness, as in fleeting loyalties.
Waver and vacillate refer to an alternation or hesitation between one direction and another. A person who wavers pauses in the face of a choice, out of doubt or indecision: She lived at home for a year, wavering between college or a full-time job. Waver can refer to the weakening of something previously strong—faith, courage, or resolve may waver, but it doesn’t have a negative connotation. Vacillate, on the other hand, can imply ineffectiveness, weakness, or instability. A person who vacillates makes up their mind and changes it again suddenly, and then changes it back again, and so on (We’ll never get started unless you stop vacillating!). Minds, thoughts, and feelings typically vacillate, which can result in vacillating policies or poll numbers. However, if your emotions before a blind date vacillate between excitement and fear, no one will judge you.