Answer
The Connectivity_Sys process only creates a background job when it finds a message in Posted status waiting in the connectivity inbox or outbox — it polls for that condition rather than always having an active job, so seeing no background job is expected when there's genuinely nothing posted yet; check the Connectivity Inbox/Outbox page for Posted messages, and if there are none, trigger the actual functional flow (like an EDI transaction or inter-site transfer) that generates one before expecting a background job to appear.