How long to process left over wine syrup?

I've got a Cherries In Wine recipe I found recommended through this forum. I've got left over wine syrup that I'd love to can, and in the comments on the recipe, many also canned it. However no one (that I saw), mentioned how long they processed it for. I'm new enough to canning that I want to double check my assumption. Since the pints of cherries in wine are processed for 20 minutes (I'm a few hundred feet above sea level,) I assume that I would process the syrup for the same length of time.

Here is the link to the recipe: https://www.yankeekitchenninja.com/2012/08/cherries-in-wine-recipe.html?m=1 (again, I found it through this forum and from the comments around it, I believe it was agreed considered safe.)

Here is the recipe if you don't want to click the link:
Eugenia Bone's Cherries in Wine

First, assemble your ingredients:
2 quarts red wine
2 cups sugar
2 cups orange juice
24 whole cloves
16 long strips of orange zest (one large orange will get the job done)
4 pounds Bing cherries, pitted

Make sure you've prepped about 4-6 pint jars and their bands by scalding them (dip them in boiling water). Get your water canner ready and have your lids simmering to soften the seals.

Combine all the ingredients EXCEPT the cherries in a large pot and bring to a boil — be sure to stir continually so the sugar doesn't burn. Add the cherries and simmer for about 10 minutes until soft.

Remove the cherries with a slotted spoon (try to pick out any stray cloves) and pack them into the jars.

Simmer the wine mixture until it is reduced by about half — about 15 minutes. (At this point, Eugenia claims it will be "viscous" but mine wasn't. Maybe I messed up, who knows.) Strain the wine mixture (to remove the cloves and zest) and pour it over the packed cherries, leaving about 1/2 inch headspace.

Wipe the jar rims with a damp cloth, set the lids on the jars and screw on the bands (fingertip tight only). Place the jars into a water bath canner and, once the water has reboiled, process for 20 minutes.

Turn off the heat, remove the canner lid and let the jar sit in the water for another minutes before removing them CAREFULLY.

Allow the jars to cool for at least 6 hours. Check the seals and you're done. Once you open them, refrigerate any leftover cherries

Again, recipe credit to the original blogger and Eugenia Bone.