The problem for me was as simple as just not knowing Javascript well. I was trying to pass the name of the id using double quotes, when I should have been using single. And it worked fine.
This worked:
validateSelectizeDropdown('#PartCondition')
This did not:
validateSelectizeDropdown("#PartCondition")
And the function:
function validateSelectizeDropdown(name) {
if ($(name).val() === "") {
//do something
}
}