What happens with the solar cycles is that during solar maxima, the sun tends to blow more ions towards the Earth (solar storms). Certainly the solar storms, and I believe also the solar winds decrease during the solar minima.
These interact with our atmosphere to create Auroras
Most of the 14
C doesn't come from the sun, but is manufactured here on Earth by cosmic rays, and high energy particles from the sun smashing into Nitrogen atoms displace a proton with a neutron.
Solar variation during the decadal solar cycles, will affect the 14
C levels, and presumably also during longer term solar variation.
Temperature changes will also affect the absorption/evaporation of various isotopes in the oceans, and thus also change the isotopes in the atmosphere.