Specifically, Native Americans don't have a meaning for the gecko. Native Americans believe that all lizards have power as a symbol of dreams and dream medicine.
The lizard is one of many Native American totem animals and is often referred to as Brother Lizard. Brother Lizard represents dreams and one's connection with the dream world. The lizard's presence in one's life signifies that it is a good time to take a look at one's shadow and see what is following one in it.
Brother Lizard spirit teaches that the process of dreaming is actually one's sub-conscious processing of all the messages one has received in a day. These messages can be about new ideas or suppressed feelings that are coming to the surface and need to be dealt with. Lizard medicine also has the potential to enlighten one on other dimensions of awareness and to give one glimpses of the future that are beneficial to one's growth. Brother Lizard's teachings tell one to pay attention to one's dreams and what they are trying to communicate.
Lizards are also a symbol of transformation and regeneration. Some Native American traditions also called on Brother Lizard as a sign of protection and self conservation.