Typically a deadlift will activate the glutes more than a squat.

If you have weak glutes then it can be a bit hard to get them to fire properly too - doing some targeted work to strengthen them may be a good idea.

I'm currently also working on my squat form, and Figure 2-8 on PDF page 18 of Rippetoe's book is instructive.

Basically, I found that to really work the glutes, I needed the hip angle (as labeled in diagram A) to be as small as possible at the bottom of the squat. This requires leaning forward at almost a 45 degree back angle at the bottom of the squat -- otherwise I can't achieve as tight of a hip angle (as shown in diagram B, if I were to remain mostly upright). As you rise, the hip angle straightens up, as does the back angle, until you're all the way upright. The key is that the back angle is only needed to not fall forward; the large change in hip angle is what you're trying to achieve.

if you sit a lot for work you may need to perform sets of stretches to activate (wake) your glutes. My preferred stretch is lying on my front, raising one lower leg to point upward, kicking the leg up towards the ceiling, and holding it there for a sec to squeeze. There are more dynamic exercises to achieve the same which i've found to be just as effective

leaning your upper body forward as you squat may also help you target your glutes and posterior chain in general