Zinc and nickel are both fairly reactive metals.
Both above hydrogen in the reactivity series of metals, they will both dissolve in acid replacing hydrogen from the acid, and dissolve into solution without added oxidizers to the acid, (mixed with other metals like copper an oxidizer may be needed).
Zinc is above iron in this reactivity series of metals.
Nickel is below iron in the series.
Once in solution iron could be used as a way to test for nickel, as nickel would be cemented by the iron metal, in a replacement reaction. Zinc will not cement with iron, as it is more reactive.
(Keep in mind this is not considering other metals that may very well be in solution, and how they will react with cementing with iron).
Pure nickel will give a color to acid (many times resembling the color of copper in solution blue to green). Pure zinc will not.
Schwerters salts used to test for silver, can give a blue with nickel, a dark brown color with brass, and brown with copper.
DMG is a good test for nickel in basic solutions (ammonia added to solution until basic) red or pink precipitate.
These can be some of the ways we may test our solution, there are others, some of which can be very complicated.
Something I may try to determine what i may have.
Dissolve in dilute nitric acid, use up the free nitric in the process, and denox solution.
Copper, brass, bronze, iron, lead, silver, zinc, nickel, tin, and other metals may go into solution.
Tin can be fairly obvious, it will form a cloudy solution and give difficulty when trying to filter.
Diluting with water can increase its results (as the tin hydroxides form), filtering can be difficult, in the filtrate a blue green color can indicate copper or nickel.
Copper and nickel can color solution blue, copper can be confirmed with added ammonia till basic, copper amine give a dark blue.
Iron or bronze can color the solution yellow, adding ammonia until basic will precipitate Iron, but will not precipitate, the metals in bronze.
Nickel and brass can color the solution a green (or blue green).
Adding ammonia until basic, add DMG, a pink or red precipitate can indicate nickel, brass gives no precipitant.
Zinc, will not color solution (as well as several other metals like Cd, Pb, Ag...), Adding a little HCl will form a cloudy white solution or a white precipitant of silver chloride if silver is present, if silver is not present.
A little sulfuric acid will precipitate lead sulfate also white powder.
In the solution making it basic with ammonia (with other metals removed or not in solution), sodium sulfide will precipitate zinc as a yellow precipitate. ( note many metals will precipitate as sulfides, so those would need to be eliminated so as not to confuse the test...