The CT doesnt have a relay in the traditional sense. It built-in to the control module (MICU), so nothing to swap out. Youre in luck, I converted my Crosstour entirely over to LED's, and I went through a dozen combinations of front/rear turn signal LED's until I found a working solution. The 1157's in the front are really the problematic ones, very few Amber with sufficient load/resistance to cooperate with the rear LEDs, which were easier to find.
Some combination worked, until you turn on the headlights/running lights (night driving), then hyperflash like crazy. The following combo(s) worked day and night driving for me.
I have a 2012 CT, hopefully your '13 is the same as far as bulb types, please confirm for yourself
For the front 1157's, I eventually got these, the only ones out of many that worked properly:
Buy Alla Lighting BAY15D 7528 1157 LED Bulbs Amber Yellow Turn Signal Lights Blinker Lamps Replacement: Turn Signal Bulbs - Amazon.com ✓ FREE DELIVERY possible on eligible purchases
Those will work with a pair of these 7440/7443 in the rear:
(the Ambers appear to be out of stock at the moment, but that is what I am currently using)
And another 7440/7443
Buy OXILAM 7440 LED Bulbs Amber Yellow 4000LM for Turn Signal Lights with Build-in Load Resistor CANBUS Error Free T20 7440NA 7441 W21W WY21W Blinker Bulb Replacement (2PCS): Turn Signal Bulbs - Amazon.com ✓ FREE DELIVERY possible on eligible purchases
Hope that helps.