Precision : seems to be a macintosh only issue .

Forum related discussion : https://www.limesurvey.org/forum/design-issues/115880-map-search-box-not-showing#171225

This is not a macintosh issue. It is an issue with using HTTPS. Is there any reason why we can't do this with HTTPS?

Yes : because https://github.com/LimeSurvey/LimeSurvey/blob/6a2ce5888be099f48da9452ef7cc85e150dd8265/assets/scripts/map.js#L225
Then any modern browser disable ajax loading in http if you are on https (security). showing search box in this condition is broken.

Must move to another API, but take time …

Would it be just a matter of replacing api.geonames.org with secure.geonames.org? I believe this is the version which supports https.

Last time i look secure need a Premium Data Subscription
You can test without to see if it work now

I tested it out, and it works.

   console.ls.log(window.location.protocol);
    // if(window.location.protocol=='https:'){
        // Currently api.geonames.org are unsecure (ssl for api.geonames.net)
       // $("#searchbox_"+name).parent().remove();
    // }
    $("#searchbox_"+name).autocomplete({
        serviceUrl : "//secure.geonames.org/searchJSON",

https://github.com/LimeSurvey/LimeSurvey/commit/19300299d1f7b2b3f6275262b3b2eeb861194ccc