I think the timeline button is added via a listener by the jrAciton module listening for the form being displayed.
Looking at it now it seams to be this function that puts the button there:
jrAction_form_display_listener()
It checks that the user has
$_user['quota_jrAction_allowed'] == 'on' in their quota profile settings, then If the user is allowed access, it checks if the module is registered to have 'action_support'.
jrCore_get_registered_module_features('jrCore', 'action_support');
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Then looking to see where this 'action_support' comes into play I find it in jrAuido in the jrAudio_init() function in this structure:
jrCore_register_module_feature('jrCore', 'action_support', 'jrAudio', 'create', 'item_action.tpl');
jrCore_register_module_feature('jrCore', 'action_support', 'jrAudio', 'update', 'item_action.tpl');
jrCore_register_module_feature('jrCore', 'action_support', 'jrAudio', 'create_album', 'item_action.tpl');
jrCore_register_module_feature('jrCore', 'action_support', 'jrAudio', 'update_album', 'item_action.tpl');
so make sure your module also has those same things in its _init() function.
See how that goes.