Drop down listbox does not exist for custom iproperties unfortunately. The only built in functionality which is a workaround is to load your multivalue text values into a parameter and then place that parameter in a local or global form. This allows selection of the parameter and that's it. To get the parameter as a custom iProperty, unfortunately you cannot use the export parameter tick box as it does not exist for Text parameters although on the wish list for years. This needs an ilogic rule either internal or external. to pass the parameter to the custom iProperty.
Form Setup:

Rule Setup

iProperties.Value("Custom", "CustomText1") = TextParameter1
iProperties.Value("Custom", "CustomText2") = TextParameter2
MessageBox.Show("All Done. Check The iProperty", "iLogic")
Another self contained method using code only is to set up a list then retrieve it using an InputListBox and then send it to the custom iproperty.
Dim List as New List (Of String)
List.Add("Text1")
List.Add("Text2")
Dim CustomText as String = InputListBox("Prompt",List, defaultEntry, Title := "Dialog Title", ListPrompt := "List Prompt")
iProperties.Value("Custom", "CustomText") = CustomText
Result

Here is a link to a video with a variation of this but using a parameter.
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Regards
Alan