Use both.
Get a roll of VHB tape and a tube of silicone from Home Depot. Be sure to wipe any loose debris and dirt off the install surface.
For the brick: Put a 1" square of tape in each corner of the sign and 1" squares centered between those. Put a few dollops of the silicone on the mortar joints of the brick if you or the customer are concerned about appearances after removal. That will minimize the amount of silicone that winds up on the brick. Silicone is easy to clean out of mortar - not so much off of brick. VHB tape is pressure sensitive and has to 'wet out' to gain maximum adhesion, so apply pressure for about 5 seconds to each area where there is tape. I believe 3M actually recommends about 20-30 seconds, but 5 will be sufficient.
For the pebble surface: You didn't say how large the aggregate is, but use the same process as above but try to use a silicone that matches the pebble (white or almond assumably). If its a rough uneven surface and not a small, smooth pebble, use duct tape as Bruce said. I would do the pebbled areas first and then go back and remove the duct tape after doing the brick areas.