Q.Trumpet vine
I have two older trumpet vines. One is getting greenery and the other isn’t showing any buds or signs of leafing out. Is it dead? They are in the same general area and have been for two or three years.

I agree that there seems to be no signs of life or growth in the 2nd vine.
Are the stems pliable when you bend them? Do they snap and break? Dead stems will break right off.
If the stems still bend, be patient and give the vine more time.
Here is an article to refresh you on the care requirements.
https://www.gardeningknowhow.com/ornamental/vines/trumpet-vine/growing-trumpet-vines.htm