Can a temporary Glasc Miscologist play units to the battlefield it died on if it's the only unit there?

Yes, if Glasc Mixologist dies at a battlefield you control, you may play a unit from your trash to that same battlefield using its Deathknell ability, even if it was the only unit there.

This interaction is permitted because of how Deathknell triggers interact with the game's cleanup and battlefield control rules:

Why this works:

1. Pending Triggers: According to Rule 734.1.d.2 and the Unleashed update clarifications, when a unit with Deathknell dies, the ability is placed on the chain as a pending item before the unit is moved to the trash and before the game performs the cleanup that would typically result in you losing control of an unoccupied battlefield.
2. Maintaining Control: Per Rule 187.4.c, you do not lose control of a battlefield while there are items on the chain. Because the Deathknell ability is on the chain, the game pauses to resolve it.
3. Playing the Unit: When the Deathknell ability resolves, you play a unit from your trash to the battlefield. By the time the game finishes the cleanup process and checks for battlefield control, you have a new unit present, which allows you to successfully maintain control of that battlefield.

Important Distinction: Attacker vs. Defender

Your ability to play the unit to the battlefield depends on your status at that location:

• If you are the Defender: You already control the battlefield. You are permitted to play the unit there to maintain your control (as established in RiftJudge FAQ #9149).
• If you are the Attacker: You do not control the battlefield until the showdown is resolved and you have successfully conquered it. Because you do not control the battlefield during the combat cleanup phase, you cannot play a unit there (as established in RiftJudge FAQ #9479).

This interpretation is supported by multiple RiftJudge FAQs (e.g., #10245, #9149, #11134) regarding the timing of Deathknell and battlefield control.