"Required" by what? Are you referring to some cultural convention or a law of nature or what? ;)

Wikipedia's example shows a D major without a seventh: https://en.wikipedia.org/wiki/Secondary_chord

In this example, I think the F# note alone works in some kind of a secondary dominant'ish function, even though it's not even a chord.

On the next line I added more simultaneous notes, leaving less room for imagination. Do these sound secondary-dominantish enough to you?

Let's make some changes:

"Required" by what? Are you referring to some cultural convention or a law of nature or what? ;)

Wikipedia's example shows a D major without a seventh: https://en.wikipedia.org/wiki/Secondary_chord

In this example, I think the F# note alone works in some kind of a secondary dominant'ish function, even though it's not even a chord.

On the next line I added more simultaneous notes, leaving less room for imagination. Do these sound secondary-dominantish enough to you?

Some more:

To my ear, the one with the C-F# tritone gives the strongest secondary dominant vibes, followed by the D-F# version. There are at least two ways to think about it. What is the implied "true" chord there - is it D7, or ... F#dim7? In the Barry Harris way of thinking, the dim7 is the "real" dominant.