I have worked with integrators at RSM US to integrate vendors and invoices. For both we utilized Maximo's REST API to allow SAGE to pull from Maximo and post back to Maximo. On the Maximo side we had to work the process to allow Sage to easily query for data when it was ready to be integrated. We did this using statuses, one to indicated it was ready to be pulled and another couple to indicate success or failure.
In my example we did not pull from SAGE but if you wanted to initiate the pull from Maximo I think a cron task calling an automation script to do the pull would be your best bet.