If there are two wingtips, there are two vortices.
Vortices - summary
There are only two vortices, produced due to the very existence of ends to the wing - the wingtips. Pressure distribution that exists over the wing ceases to exist beyond the wingtips (since there's no wing beyond the wingtips). To understand this in detail, first consider 2D flow.
In 2D, the low pressure region on the upper surface of the wing sucks the air from all four directions: It pulls the air from ahead, causing it to accelerate and upwash. It pulls the air from behind, causing it to decelerate (this is the pressure recovery). It pulls the air from up above, causing it to downwash. And in an attempt to pull the air from underneath, it pulls the wing up, thus producing lift.
In 3D, this low pressure also tries to pull the air from sideways. On an infinite wing, the pressure distribution is homogeneous spanwise, and so there is no spanwise flow. On a finite wing, there are two wingtips, beyond both of which there isn't a similar pressure distribution. This causes the low pressure region above the wing to pull in the air from beyond the wingtips. The high pressure region underneath the wing similarly expells air outboard, beyond the wingtips. This is what causes wingtip vortices.
High Wing Configuration
On a high wing aircraft, on the part of wing above the fuselage, there's still a region of low pressure (and even if that portion on its own didn't have a low pressure region, the pressure from the consecutive parts of the wing will be carried over there). More importantly, this part of the wing is not like a wingtip, and shouldn't be treated like one; there is only one wing, and two wingtips (the "left wing" doesn't terminate at the fuselage, it extends from there all the way to the right wingtip). Since there are no wingtips in the middle, there are no vortices.
You can think of it this way: both the "left wing" and the "right wing" try to form a vortex in the middle; the two POTENTIAL vortices are equal in magnitude but opposite in direction. The two potential vortices completely annihilate each other, and so there's no vortex in the middle. (you can apply this idea at any point on the span, except that the two opposing vortices won't always be equal in magnitude; they are only equal at the middle of the span. If you do this for every point, the end result will be the two wake vortices as we know them)
As far as your handbook's claim goes that the fuselage acts as an end plate, restricting the vortex formation - yes, that's technically true: the fuselage will act as an end plate for the left wing¹, largely inhibiting it's vortex. But the right wing will do a better job at this, eliminating the left wing's vortex altogether, as described earlier. If anything, fuselage is actually making the situation worse by not letting the right wing properly do it's job (that's why the two small vortices form in first place).
¹same is applicable for right wing