About handling, I am one of those who think its not a good thing EVER. To understand that, what does it mean? It means, handling never benefits the monitor, it only benefits the human.
The vast majority of monitors spend their lives going about what monitors do and never and I mean never get or want to be handled by humans or any animal considered a predator. So surely its not something normal to their lives. Its abnormal.
It effects behavior, which means, its not a, one or the other thing, or good or bad thing. It effects behavior which also means the vast majority of humans, and that includes the smartest of the academics, do not understand the effects. In my opinion, it never ranges into the good side of good and bad. Many times it ends up causing the death of captive monitors. More a longterm stress effect.
A while ago, years, I read of all these tame monitors. So I did my normal casual investigation. I already knew how to take a monitors heartrate. Their heartrate is an indication of their real condition, much like yours is. So I took heartrates. Funny thing was, those tame lap sitting monitors ALL had elevated heartrates. Speeding actually. Which did not indicate being tame. But indeed indicated a fear responce.
What that means is, we may not understand what is tame and what is a natural predator responce. Again this has millions of degrees. But I suggest learning to take your monitors heartrate. This in help you understand what your monitor is feeling.
When holding your monitor, place your good hand(both of mine work well) under the monitors belly. Place your most sensitive finger about halfway between the front and back legs. A tiny bit closer to the front legs. Then lift that finger slighly. You will feel a little hard knot beating like crazy. Rarely not beating like crazy. hahahahahahaha
Next, I have seen tame monitors and one shining example was a beautiful nile. This person would drive around with it on the dashboard of his car. This person would leave it parked outside sitting on the dashboard. Hmmmmmmmmm. While they thought that was an expression of tameness. They could also set it anywhere and it would not leave, I again question that as being tame or normal.
In this case, its a little different. Monitors are a bit like a ferret or kinkochew-thing that MikeT has, they are wonderful cuddly things twice a day, as they wake up and as they go to sleep. The rest of the time, they are into everything they can get their nose into. Well, thats what healhty monitors do, when healthy and up to temps, they GOT to know what the heck everything is. They GOT to stick their noses into everything stickable. So what bothers me is, a healthy monitor WILL NOT SIT IN YOUR LAP, at least for anything more then a few seconds or minutes. It will want to see what the heck is all around. IT HAS TOO. Thats what monitors do.
ALso I am one of those people who think monitors are naturally tame. As far as I can tell, they get over their fear of things very very quickly. They also are not biters Naturally. Even wild ones get over biting you very quickly. OK, some don't. But most do.
In captivity, ones that bite, normally have good reason to bite. They normally have been major league offended and feel that is the best course of action. Yes, normally rightfully so.
My monitors are always tame. All of them. But they do not like to be picked up and under a monsters control. I have had wonderful folks over like Jefe and Rsg, and showed them this. I can go pick up a male(an example) I normally grab them by the base of the tail(as they scratch everything in sight) they flop and twist and do this swimming deal. They appear all crazy. But as soon as I place them in back in their cage, I mean as soon as their front feet hit the ground, they are either eating, looking for food or attempting to mate the female. Again, they were flopping like a tuna out of water. Also, I can hold them up high and they completely stop this flopping deal. They quickly take a high position and view the surroundings(a monitor monitoring) All monitors love this, they need this, gotta have it, they got to, got to, got to, whoops a little dock of the bay slipped in. A real need for monitors is to monitor. I know that sounds odd, but I get the feeling thats why they named monitors monitors, to monitor and all. This is a most important behavior.
So I have found that monitors learn to tolerate, they learn to use you(like a cat) but to be tame and want to be around you, I am not so sure of, well only if you have something they want. I do not see monitors run TO people when having a fear response, you know, a safe place. They always run to a safe place.
So handling is not a benefit, not at all. Of course if you have one that tolerates you and you have food, or its cold and you have warmth, or you have all sorts of smells on you, hmmmmmm this gets dangerous with large monitors. Or a female thats into heavy cycle and your a male(sad but true, monitors are not picky) or if your a female and the subject is a male monitor(iggies do this too) but again, those are things they want.
So No, neither your timor or niles want or need to be handled. Although both could learn and want to handle you. Yes, it would be very easy to train them to take food off your shoulder(done that many times) I may suggest wearing some sort of ear guard. Cheers