The Dropdown jelly form does not use the name attribute. This makes it difficult to reference in selenium tests. Similarly to what dropDownListSelector does it should have something like

<td class="setting-main">
 <!-- create drop-down list -->
 <select class="setting-input dropdownList" name="${attrs.name}">
 <j:set var="dropdownListMode" value="createSelectField"/>
 <d:invokeBody/>
 </select>
 </td>

in its jelly file.

For all config files using a dropDownList in fact the Form Element Path plugin does not generate the path correctly (it would simply add "/" or "/" followed by a number cause it cannot compute the unique id using its name). For an example see https://github.com/jenkinsci/acceptance-test-harness/blob/47ae4d5cd6e1c17308c1dc2e28ee6b3b11bc3a0d/src/main/java/org/jenkinsci/test/acceptance/po/DumbSlave.java#L23

Besides that, the name field is defined and not used in the jelly file.

However, note that fixing this will make all selenium tests which use the form path plugin on dropdownList (ass SSh slave plugin selenium test) fail. Fixing this will require a fix of all of them with the new path.

I am not sure it's worth it.