Webform contact autocomplete only searches the first character of external ID
For a large org who also could not use any Name autocomplete (just too many Contacts) - I create a Enter Contact ID Form Widget (for _contact_existing). If you adapt your processes to do lookup by Contact ID - this new Widget is in current versions of Webform CiviCRM module. If you continue to want to lookup by External ID - have a look at the code and mimic it after this example or alternatively sponsor a bit of time and we'll be happy to get that done for you.