To do this problem we must first realize it is nothing more than a speed-time-distance problem, or perhaps more accurately an "echo" problem. We are sending a wave out from a source and waiting for the return echo. We must also make some simplifying assumptions. For example, we will assume the Earth is at its average distance from the Sun of approximately 146x10^9meters and that there is no delay in receiving and sending a reply message at the Huston end (an automated response which is sent as soon as the incoming message from the Sun outpost is received, for example).
The relevant equation would be
s = d/t where s is the speed, d is the distance for the round trip, and t is the time we wish to know.
s in this case is the speed of electromagnetic radio waves = 3.00x10^8m/s
d is twice the distance between the Sun and Earth (there and back) = 2.92X10^11m/s
Solving the equation for t gives us
t = d/s = (2.92x10^9m/s)/(3.00x10^8m/s) = 973 seconds = 16 minutes 13 seconds.
Thus, the astronauts would have to wait a minimum of 16 minutes and 13 seconds to get a response.
Because radio waves and visible light are examples of electromagnetic radiation and all electromagnetic radiation travels at the same speed through space, it would make no difference if the astronauts tried to send their messages by manipulating the light from the Sun.