Your dealer is doing you a disservice with his erroneous information. It needs adjustment or lubrication.
Also be aware that if it is barely engaging, it rounds off the cogs on the diff lock. Sounds like yours isn't even engaging that much. When adjusted properly, these work just as described by several folks already. Stop the wheels from spinning entirely, try to engage, if cogs are not lined up, spin a wheel slowly and in less than 1/4 turn of a wheel, the diff lock pedal will drop a little more and you are engaged.
If you engage while the wheels are spinning fast, it is easy to damage the cogs as it rounds off the edges, then the diff lock will not want to stay engaged, even with increased foot pressure. So do be careful with that.
For those of you with older 3016/3616 and 1526, if the diff lock cog does get damaged, the tractor does not have to be split to fix it, but the right side axle housing does have to be removed. It's a few hours work, but nothing crazy.