How can I create a location in nginx that works with AND without a trailing slash?

It might be in the regular expression that you're using --

location ~ ^/phpmyadmin/(.*)$

The above will match /phpmyadmin/, /phpmyadmin/anything/else/here, but it won't match /phpmyadmin because the regular expression includes the trailing slash.

You probably want something like this:

location ~ /phpmyadmin/?(.*)$ {
    alias /home/phpmyadmin/$1;
}

The question mark is a regular expression quantifier and should tell nginx to match zero or one of the previous character (the slash).

Warning: The community seen this solution, as is, as a possible security risk

The better solution:

location ~ ^/phpmyadmin(?:/(.*))?$ {
    alias /home/phpmyadmin/$1;
}

Ensure that server has permissions to /home/phpmyadmin first.

Explanation of difference with accepted answer:

It's all about regular expressions.

First of all, the ^ char means that you want to match from beginning of string and not somewhere in the middle. The $ at the end means matching to the end of the string.

The (?:) means non-capturing group - we don't want it in the capturing results, but we want to simple group some chars. We group it like this, because we want the / char to be a nonsignificant part of the child path, and not a significant part of the parent path.