I’m glad you got it working! Just a heads up, the code snippet you provided actually targets all input fields on the entire site and updates their placeholder text color.
Perhaps that might not be your intention and thus it may be good to add some specificity to your selector.
For example, if you are aiming to target the search input in the search menu only, you can do something like this:
.search-menu #search-term::placeholder {
color: #hexcode;
}