Phillip
You are not joking when you say there are some others.. Don’t know if these are of interest but, from my directories , only going up to 1873 I have::
 
1845                Eaves Alfred, watchmaker, 157 Livery st
1849-52           Eaves Alfred . watch & clockmaker, 15 Prospect row
1855-68           Eaves Alfred . watch & clockmaker, 1 Lancaster St
1872-73           Eaves Alfred. Augustus, watch & clock maker, 147 Gt. Lister st
 
1862                Eaves, Arthur Frederick, clockmaker, 36 Lombard St
1868                Eaves, Arthur, clock manufacturer. Emily St
1872                Eaves Arthur Fredk. clock & clock case maker, Emily street
1873                Eaves Arthur Fredk. clock & clock case mkr. 139 Emily st
 
1845-49           Eaves Charles watch & clockmaker ,106 Lancaster St
1852                Eaves Charles watch & clockmaker, 160 Broad St, Islington
 
1872-73           Eaves Francis, clock & watch maker, 1 Lancaster street
 
1872=73          Eaves John, watch maker, Park road, Aston park
 
 
1849-52           Eaves Joseph, Watch hand maker , court 13 Cardigan St
 
1862                Eaves, Mark M.. clock bezel maker, 2 Salop St
 
1858                Eaves, Samuel, watchmaker. 6 Gt. King St
1867-68           Eaves, Samuel, clock & watchmaker, 51 Belmont Row
1872-73           Eaves Samuel Spilman, watch & clock maker, High street, Aston New town
 
1852                Eaves Thomas, metal turner. court 4, Birchall street
1855                Eaves Thomas, clock bezel manufacturer, 43 Cheapside (PO dir only) 
1855                Eaves Thomas, clock bezel manuf. court 4, Birchall street; h. 116, Moseley street (Whites dir only)
1855                Eaves Thos. P. watch & clock maker, 160 Broad st. Islington (PO & Whites dir.)
1858                Eaves Thomas, clock bezel maker, home: 43 Cheapside
1858                Eaves Thos. jun, clock bezell maker  h, 47, Brewery at, Darwin at
1858                Eaves Thomas and Son, manufacturers of clock bezells. and clock materials generally, 684, Moseley st
1862                Eaves Thomas, clock bezel manufacturer, 43 Cheapside
1862                Eaves Thomas Arthur,clock bezel maker, 67 Moseley St
1867                Eaves Thomas (senior), clock bezel manufacturer, 43 Cheapside
1867                Eaves Thomas Arthur, clock bezel maker, 92 Charles Henry St        
1868                Eaves Thomas Arthur, general cock founder, manuf. of plumbers brass foundry, steam fittings, beer machine etc., clock materials & bezels,bell founder, Princes works, Charles Henry St
1872                Eaves Thomas Arthur, brass founder 91½ Charles Henry St 
1873                Eaves Thomas Arthur, brass founder 92 Charles Henry St    
More from 1876 on
 
Note
For 1855 there are the whites and the Post Office directories. Probably surveyed 
at slightly different times, so have marked on these results which is which. Several 
Thomases, so have put together. I think some were brassfounders before becoming 
clockmakers, but cannot be sure it was same people so have omitted.
If later Eaves entries are of interest then let me know and i will go further on