Gulfstream IV general aviation First Officer reported a landing gear malfunction on the ILS approach and the crew performed a go-around. The crew lowered the gear with the alternate gear extension procedure and landed safely.

Narrative

Ferry flight ZZZ1 to ZZZ. The flight was uneventful until the gear was selected down on the ILS approach. Flaps were already selected to 20 degrees. With the gear handle down it remained red and nothing happened; then multiple yellow CAS messages appeared. Nose gear not down; L-R main gear not down; and L Hydraulic Quantity Low. A missed approach was initiated; the tower confirmed we had no gear visible; and we were given a heading and climb to 2000 feet. We requested vectors to remain in the area and stayed at 2000 feet for the remainder of the flight. On the missed I had selected Manual speed 200 and we remained at that speed electing to leave the flaps at 20 degrees until we sorted out the low left hydraulic quantity. We reviewed the CAS messages and consulted the hydraulic synoptic which indicated the Left reservoir was at 1.8 gallons. We decided to raise the gear handle back to the up position to agree with the current position of the gear. All CAS messages disappeared as if we had no issues including the low quantity warning on the synoptic; now showing the left hydraulic full. This made us think its not a fluid level issue. We decided to try the gear down again and received all the same indications and CAS messages. At this point we had 3000 lbs of fuel and we agreed it was time to run the checklist from the top so first was the Nose gear failed to deploy which ultimately bring us to the alternate gear extension. We requested priority handling and requested the trucks for our landing. The emergency gear extension procedure was successful and we conducted an uneventful approach to runway XX. After landing we decided to pin the gear before taxing in just to be on the safe side.Cause: Potential hydraulic system errors/failures - internal and unknown. Suggestions: Unknown - abnormality within the landing gear/hydraulic system. Pilots tried troubleshooting the issue in a controlled environment to no avail. Checklist lead us to extend gear with alternate emergency procedures as trained. Proactive/preventative maintenance could be a solution.