Here's my intended answer.
To determine whether an object is Likewise or Unlikewise, start by performing the following procedure:
Orient the object (and yourself) so that the top side of the object is facing up, the front side of the object is facing towards you, and you are facing towards the object.
The object is Likewise if
the left side of the object is on your right side, and the right side of the object is on your left side.
The object is Unlikewise if
the left side of the object is on your left side, and the right side of the object is on your right side.
The object is Funny if the procedure cannot be performed.
Explanations of some of the examples:
The most common examples of Likewise objects are animals with bilateral symmetry (including humans); sculptures of these animals; items of clothing and apparel; and vehicles. These objects all have an implied direction of motion, and this direction defines which side is the front. To quote hexomino's answer, for these objects, left and right are defined "from the perspective of the object".
Unlikewise objects are usually inanimate objects that are viewed, or used, from a particular direction. This is what defines the front of one of these objects: the front side is the side from which the object is usually viewed or used. For these objects, left and right are defined from the perspective of the viewer or user.
Funny objects usually don't have a front, a back, a left, or a right. There are a few exceptions. For example, standard playing cards are usually printed in a rotationally symmetrical way, making it impossible to define the "left side" or the "right side" of the card, and so these cards are Funny. But they certainly have a front and a back.
Mount Rushmore is a difficult case. It's a sculpture of some people, so "left" could be defined from the perspective of the object. But it's also an object which is always viewed from the same side, so "left" could instead be defined from the perspective of the viewers.
A Magic: the Gathering card is another difficult case. Unlike standard playing cards, Magic cards do have a clearly defined left and right side when you look at the front. But it's not clear what "the left side of the card" means when you're looking at the back of the card. Does it mean the side which appears on the left when the card is viewed from the front, or from the back?
One more potentially ambiguous case would be a painting of a person. These have the same ambiguity issue as Mount Rushmore. (This Wikipedia article is relevant: https://en.wikipedia.org/wiki/Proper_right) This is why I specifically gave The Starry Night as an example, rather than just "a painting": since The Starry Night does not depict a person (or any Likewise objects), it's unambiguously an Unlikewise object itself.