You did not tell us that the CD4066 is permanenly shorting its contacts. Instead you told us that its on-resistance is too high.As i said, CD4066 not working well because its permanently shorting this 2 pads...
Then the CD4066 is defective or you forgot to connect the GND of the CD4066 to the GND of the microcontroller circuit.
The switch contacts of the CD4066 must have a voltage that is between its GND to its positive supply. Then it should work to make a logic high in the microcontroller circuit for 5 seconds if the GND of the CD4066 is connected to the GND of the microcontroller circuit.
When the 555 output and the control pin 13 of the CD4066 go almost to GND after the 5 seconds timing then the contacts of the CD4066 should be open, not conducting.