The ground frame will come under the control of one of the signalboxes - that will be the signalbox the person operating the ground frame will liaise with.
With absolute block, the usual arrangement is for the controlling signalbox to release the ground frame, either mechanically or electrically. The ground frame would normally have an indication of the release, but no block indication. The controlling signalbox would be responsible for sending the appropriate bell codes to the signalbox at the other end of the section for trains entering or exiting the siding.
With the various forms of single line control, the release will depend on whether or not trains can shut in. In the simple case where trains can't shut in, all that is usually needed is authority to use the ground frame for shunting. In some cases this can be purely verbal, in some cases the controlling signalbox gives an electrical release. It was common to provide a track circuit, so that the ground frame could only be operated once the train had arrived at it. If trains can shut in, the ground frame will also need to be released by the block controls, so that the ground frame can't be released to let a train out into an already occupied section. However, that doesn't mean that a block instrument will be provided at the ground frame. As at Foley Park, a simple two position needle indicator is all that is usually provided to show that the ground frame is free to be used or not.
Note that there were at least four different versions of tokenless block (WR, SR, ScR, and BR). Likewise there were regional variations on how things like direction and acceptance lever controls were implemented. So I can only generalise, there are likely to be many variations.
For example, Foley Park has an Annetts key instrument for releasing the ground frame. The Western tended to favour Annetts key releases on ground frames, whereas some other regions tended to provide an electric lock direct on the ground frame lever rather than provide an Annetts instrument.