Call me crazy, but I plugged a solution of Hydromorphone (Dilaudid) one night when I was working back when I was in college. I had gotten a little too audacious in terms of my pill-to-vehicle ratio. I really didn't have much experience injecting pills either, still don't, so I was asking for a fuck up. I think I had 4-5 4mg Hydromorphone in the rig, ready to go, when a clog occured in the needle. It was my only rig and I had already been in the bathroom of a busy restaurant for about 10 minutes figuring shit out. I said, "what the fuck", broke the needle off, inserted and plunged. I wasn't laying down or anything. I immediately walked out and got back to my cooking job, which can be physically rigorous. My shot hit me just fine, albeit not with the intensity of an injection, but a hell of a lot better than oral.
My point is, you don't necessarily have to be laying down if you're in a tight spot like I was. Without getting too detailed, the anal sphincter is capable of retaining liquid. However, the smart thing is to eliminate the potential for mishap by placing gravity on your side. I tend to lay on my stomach, but it seems like most others prefer laying on their side. I don't think that there will be a significant difference from one position to another.
As to how far the syringe should be inserted inside before plunging, that's a matter of some conjecture. I've never made it complicated and generally go by feel. I insert, go a little farther, 1 - 1.5 inches maybe? I've never had a mishap with plugging if that makes you more confident. If you're dope sick, obviously you should try to go before you plug, likewise, if you're very constipated like an Opioid addict might be, then plugging might not be totally feasible due to the potential of your solution being absorbed into the feces and then the feces being expelled.
Rectal Admin or "Plugging" is like the gospel to me and a perfect example of Harm Reduction. You get some benefits to bioavailability and intensity just like you might from injection without many of the inherent risks.