Try this :
(1) access the root service of an activated Task Gateway service on SAP NW Gateway (mine is SP09 and I am using version 2 of the Task Gateway service) - that should be a URL like : https://<myserver>.<mydomain>/sap/opu/odata/IWPGW/TASKPROCESSING;mo;v=2/
You will see a SubscriptionCollection and a NotificationCollection and the TaskCollection has an indicator saying it is subscribeable
(2) In SE24 locate the data provider class for the task gateway service (/IWPGW/CL_TGW_EDP_TASK_V2) and look at its inheritance tree
/IWPGW/CL_TGW_EDP_TASK_V2 inherits from /IWPGW/CL_TGW_EDP_TASK, which inherits from - surprise surprise - /IWBEP/CL_MGW_ABS_DATA
That's rather awkward cause - as the root service tells you the service supports subscriptions - one would normally expect to find an inheritance tree climbing up to the base class /IWBEP/CL_MGW_PUSH_ABS_DATA, as all other services do when they support subscriptions.
Not so with the Task Gateway service
(3) Use a REST client to try and create a subscription for the TaskCollection in the Task Gateway service
Result : KO, It doesn't work (at least not for my setup)
To summarize
=> OBSERVATIONS
(1) the root service tells you, you can subscribe to the TaskCollection in the Task Gateway service
(2) the provider class however doesn't appear to have the right inheritance to do so
(3) when trying to create a subscription, things blow up in your face (as you would expect considering (2), but not in an honest way cause (1) promises you, it can
=> QUESTIONS
(1) How to explain the availability of the SubscriptionCollection / NotificationCollection in the root service ?
(1) Are subscriptions supported or not - because of some technical limitation
(3) If one would like to subscribe to the TaskCollection in the Task Gateway, would it be possible to enable this by changing the inheritance tree ?
(2) If it can work, how does the subscription process work considering Task Gateway service is a moc (multiple origin composition) service - assuming that during the creation of a subscription, the gateway - according to SAP help - contacts the backend system to validate (authorize ?) the request.