Taxonomy Menu - non-default taxonomy doesn't update menus

The problem that I'm facing is that when I create a new [taxonomy] vocabulary, I cannot get the terms to appear in a [taxonomy] menu. I don't have a problem if I add new terms to the default/existing "Product Category" or "Collection" category.

This may be related to:
Taxonomy Menu requires full menu rebuild after install to work. I think this is nearly a duplicate of that issue, as far as the discussion there is headed. I just wanted to create this, since technically the subject of that issue is resolve and this deals with a slightly different issue, which I think could be treated separately.
and possibly Menue path type with Commerce Kickstart Taxonomy

I've reduced this to a problem relating to kickstart. Installing only Drupal core, I cannot reproduce this. That sentiment is supported in Taxonomy Menu requires full menu rebuild after install to work, which mentioned that rebuilding the menu might help. I could not get any amount of rebuilding menus to assist in getting a new vocabulary's terms to appear in any menu. That issue also refers to Menue path type with Commerce Kickstart Taxonomy, suggesting that the taxonomy may need to be referenced by a product, and appear in the Search API. Theoretically, that shouldn't be the case, but I guess I'm going to see if I can test it to see if it might actually provide a work-around.

I also have a thought to disable, then re-enable the taxonomy menu module, but I ran into problems with that in a previous install; the module couldn't be unchecked and I didn't want to go through the trouble of trying to remove the menus I created.

On a clean install of commerce_kickstart, without the store functionality and with no options checked, I get the following in the search API:

Product display

Status
enabled (disable)
Machine name
product_display
Item type
Node
Server
Frontend
Index options

Cron batch size
50 items per cron batch.
Indexed fields
Node ID, Content type, Status, Date created, Date changed, Title, Product, Product category, Item language, Product » Price » Amount (decimal) (Min), Product » Price » Amount (decimal) (Max), Title (Fulltext) (1.0 x), Product category name (Fulltext) (1.0 x), Product category » Name, Product » Price » Amount (decimal)

Configuration status
Default

I create a reference to the new taxonomy I created in the existing Product Display content type. Back in search API, the new taxonomy didn't appear, but if I edit the Product Display, I was able to add it to the indexing.

Tried rebuilding the menus, still they don't appear.

I tried to disable all taxonomy terms which were assigned to create entries in a menu. I couldn't disable the module (this may be hardcoded).

I disabled Commerce kickstart taxonomy module. Then, I was able to disable Taxonomy menu. I re-enabled them.

First the test vocab. No new items appear in menu.
Then, enable Product categories item. The product categories appear in the menu, but not the test.
Rebuild test menu on save. No new items appear in menu.

I don't think the indexing is relevant to this issue; on a basic Drupal-core install, I can add the taxonomy and add them to the menu, without adding any content (with which to reference the taxonomy with).

Let me know if you have any suggestions. I'm open to testing things in my environment.

(Possible) workarounds:
I might start looking again into building a commerce site from scratch (each module installed individually).
Alternatively, if I can get away with renaming the existing vocabulary, I can probably use it for my site, which is fairly simple.