Well, you did ask what I liked to do when "sparring." For me, "sparring" is practice, or laboratory time. It's a time to try new things, a time to perfect other things. It is not a time to "win."
Usually, the instructor has us work on some technique or combo whatever for a bit before we start sparring. I always like to then try what we just practiced. So, I will give my partner the exact opening that the technique or combo of the day started from, to let my partner do it first. When things go well, they recognize what I am doing and feed me the same thing in return. So we get to learn to recognize the opportunity and then respond with what we just learned. As we get better, we gradually increase the resistance and try to counter and reverse... then throw in other stuff... then surprise them and come back.
I also like to get more practice in areas I am bad at... specifically the ones I have the hardest time working from. I usually have a hard time passing guard... so I make it easy for the other guy to get me into their guard... then I try working out of their guard. When I find that something is working really well for me, I try not to use it and try to use other things instead. When I was younger I got really good at tomoe nage. For a while I threw everyone tomoe nage. (It was especially fun when I worked with people that told me how simple and easy it was to defend and counter.... I heard some very interesting "kiai's" as they flew over me...) But, I had a hard time with most of the other throws. I had to force myself not to take the easy throw, but to work on the harder ones. This is not the way to tap or beat every person I spar with. But, it is a way for me to improve my techniques and to practice what I just trained a few minutes ago or what I have been having a hard time with.