ICC for repeated measures across time with clustering by eye

Question

I am trying to assess the ICC across measures at 2 time points (baseline and 2 months) on participant eyes, so each row represents an eye and some participants have two eyes included in the study.

I have been able to use the ICC() command from the psych package in R as follows:

> head(data1) 

  ID   eye  var_baseline var_2months
    1   L    75          63
    1   R    56          67
    2   L    54          NA
    4   L    78          61
    4   R    60          65
    6   L    80          81


> ICC(data1[,c("var_baseline","var_2months")], missing=TRUE, alpha=0.05,lmer=TRUE) 

I am using the ICC(3,1), so thats assuming time points as fixed , where I am interested in the consistency of the measures across these 2 timepoints.

Q: How do I account for the additional clustering by eye in the ICC estimate?

I have fit a lmer model with the following formula after reshaping my data to long format, specifying the nesting structure in ID and eye:

formula1 <- var ~ time + (time | ID/eye)

m1 <- 
 lmerTest::lmer(
 formula =  formula1,
 data = data.frame(data1),
 control = lmerControl(check.nobs.vs.nRE = "ignore"),
 na.action = na.exclude
 )

My random effects looks as follows:

Random effects:
 Groups    Name        Variance Std.Dev. Corr
 eye:ID    (Intercept) 25.0782  5.0078       
           time1        5.5080  2.3469   0.15
 ID       (Intercept) 30.5598  5.5281       
           time1        0.3977  0.6307   0.32
 Residual               6.9562  2.6375  

I'm uncertain about calculating the ICC with the provided variance components. Alternatively, would it be appropriate to fit a model without time as random slopes, utilizing the following formula in lmer:

var ~ time + (1| ID/eye)

The above model has the following random effects:

Random effects:
 Groups    Name        Variance Std.Dev.
 eye:ID    (Intercept) 23.143   4.811   
 ID        (Intercept) 31.354   5.600   
 Residual               9.893   3.145 

Is there a method available to calculate the Intraclass Correlation Coefficient (ICC) for two repeated measures (at two time points) while accounting for clustering, such as the presence of two eyes within a participant?

Thank you, any help on this would be much appreciated!