Where to programmatically enable a Feature module I created a Drupal 7 feature and usually I would enable it with Drush, but someone suggested that I enable it with an update hook (which I assume means it gets enabled on updb or update.php).

I saw this discussion on enabling modules programmatically How do I programmatically install and enable a module?, but it blithely skips over where to write the code. Does it go somewhere in the installation profile? Does it have to be called from another custom module that is already enabled?

I'm actually an experienced Drupaler that has somehow managed to miss this one crucial lesson, I've just been using Drush to enable modules but I want to do this the best way.
A feature module is just another module. And you can enable it programmatically using the linked code from another enabled module's hook_update_N placed in this another enabled module's *.install file. This even can be another feature module. Then have this hook fired via drush updb on the command line or by visiting your site's /update.php.

You also could do that from a form submit handler. Or even from a menu callback providing some custom endpoint you can access with cURL for example.

It's safe to use other feature modules' *.install files. Since Features never touches *.module and *.install files during regeneration. So you are free to use them to your needs.