Turn signal indicators both light up when either signal is selected

On my way across the mountain pass the other day, I turned on my left signal to change lanes. I noticed that my right signal indicator was also blinking (though very dim). The right signal being on also illuminates the left. This is an intermittent issue, and so far my theory was heat under the dash causing some thermal problem. Turned the heat off, no change. The outside lights do not do anything abnormal. If you shut the van off, and start it again, they work fine for a short amount of time. But, the problem is still intermittent. Even smacking the dash does not have an effect on this. Any possible solutions?