How do I turn on search highlighting from a vim script?

Just found out the answer myself:

call search(l:searchString)
call matchadd('Search', l:searchString)

The

feedkeys()

function is the key (pun intended):

call feedkeys("/pattern\<CR>")

or cleaner:

" highlights – or doesn’t – according to 'hlsearch' option
function SearcH(pattern)
    let @/ = a:pattern
    call feedkeys("/\<CR>")
endfunction