Red Mountain follows a road with many switchbacks up to a lookout building for about 1.25 miles. This section of the trail gets out of the tree line quickly and is exposed for the majority of the hike ( I would suggest a windbreaker jacket for this reason). From the lookout, you can see a fairly obvious trail that follows the ridge up to Red Mountain. This part is short but very steep and isn’t for the faint of heart as you can see how quickly the sides of the trail drop off. Though, it is a short hike up to Red with outstanding views of Table Mountain and Monument Peak. You could add on to this hike by continuing to Monument Peak and then Table. This trail gives you a major bang for your buck.
If you don’t have a high clearance vehicle, you can tack on about 3.6 miles extra (round trip) and hike up the rough part of the road. I would park here if you do not have a high clearance vehicle. This would make your hike about 7 miles round trip.