Try creating eraser preset and select them. You can only select tool preset for the current tool. If you have unchecked current tool only. You can select any tools Preset. Photoshop will first switch to the correct tool then set the settings recorded in the tool preset. If you record the select brush Brush preset into an action and Current tool only is checked and the current tool is the eraser tool the action will fail with select is not available. If current tool only UI is unchecked Photoshop will first switch to the brush tool and select will be available. The Brush tool will be the current tool with the preset settings set.
Why doesn't the tool allow adjustments w/o having to go make something else do it? Makes zero sense to have a non-adjustable eraser tool.