Rather than look up the element, remove the probe, look at where the water high level is to verify normal operation. You can also bleed down the steam tank via the right hot water wand, then after refill turn it off and let it cool. Then look at the water depth. To find the element top either probe with something soft like a chopstick, or pull the water out of the water sensor hole with a "cooking baster" or some other pump. Look with a flashlight.
The water sensor/gicar refill is not unique to the Duetto, it is common to dual boiler machines.

Not sure I understand the statement "From the moment my technique when I made latte is to purge from water tube 0.5 liters of water" Are you saying you have purged into a container and measured 0.5L of water from the steam wand? That is a lot of water and steam and would take a long time, many minutes....A fresh purge from the steam wand into a heavy glass measuring cup yielded on my machine ~15-20ml in 30sec. How do you get 500ml? Also I am describing a US 110v model with a different element than the 220v European model. The Euro version has higher wattage (1500w vs 1200w from memory) which I see as a benefit. The internal wiring has 1/2 the current given the same watt draw, which results in less termination and wire heating and quicker water heating recovery.
My understanding is, when the water drops below the tip of the sensor it refills, and when water contacts the element there is a delay. The refill delay is what I am describing. If you drain the tank with the water wand the refill will start even when the valve is still purging.
I would not recommend purging continuously for many minutes in an attempt to expose the element.
One of the reasons this machine is so good, is the use of commercial easy to locate off the shelf parts. It is no surprise you don't see a unique part number reference. If you search on coffeetimeuk you will find some very excellent reference material from Dave on this machine. Also if you search you can find schematics of at least the earlier duetto which is very similar except for the relays and dual pid vs pressurestat.

You can also increase the pressure up to 1.5bar. This will raise the steam temperature and possibly result in "drier" steam or at least greater expansion of the water molecules after leaving the tip.
Perhaps what you are describing is a spurty behavior of some(?) duettos. The steam has some interspersed more dense steam after purging. Mine does that to a degree. That has been described by others and may be a characteristic of the machine. However my steaming results are excellent.
Since you are an engineer/designer you want to understand the "how" from a design sense. If you use the machine and educate yourself on technique, you should, as others have, be able to get great cappuccino foam. Thats the goal
Go look at a shootout done last weekend by Dan Kehn and company in this forum.....
Cheers

sorry from my english, I dont purge water from steam wand, I purge=drain=bleed down via water wand.And I drain 300-500 ml , and after is ok from steam, I made milk foam very good.I repet, possible the maximum level of steam boiler is too high, from safety reasons.Now , the probe is maximum inside, same in previous photo, but the effect is not big.
From the moment machine function ok,( I use tank and good water San't anna ).I 'm accommodated with all,to be honest is not a big deal, is possible to be concentrated from another aspects, alex is a perfect robot.I agree my first impression when I saw all this little problems was to be upset , but now he start to like me more and more .
I use from the moment a gaggia MDF grinder, and is possible from this reason I don't have a spectacular results , but every time the machine have a idle of 45 minutes minimum, and the results is very constant.From a cold room, 15 degree celsius, what offset is ok from PID?I use offset 9C, and 93C from t1.

It sounds like you should check your water level as described above. Replacement probes, if you have to buy , are very inexpensive and they are common. You can trim them to length.

Search for tips on use. Look over on that other coffeegeek forum as well. Lots of info on offset, temp stability, heating up, purging, backflushing, cleaning, etc.
For instance, to speed heat up put a towel or tea cozy over the e61 head....can shorten to 20 minutes from ~50 minutes.
Also, offset typically is 18degF. You can convert to C.

We are all learning!
Cheers